http://computers.stmjournals.com/index.php?journal=RRDMS&page=issue&op=feedResearch & Reviews: Discrete Mathematical Structures2020-01-10T11:56:04+00:00Sugandha Mishrasugandha.mishra@celnet.inOpen Journal Systems<p align="center"><strong>Declaration and Copyright Transfer Form</strong></p><p align="center">(to be completed by authors)</p><p>I/ We, the undersigned author(s) of the submitted manuscript, hereby declare, that the above manuscript which is submitted for publication in the STM Journals(s), is <span>not</span> published already in part or whole (except in the form of abstract) in any journal or magazine for private or public circulation, and, is <strong><span>not</span></strong> under consideration of publication elsewhere.</p><ul><li>I/We will not withdraw the manuscript after 1 week of submission as I have read the Author Guidelines and will adhere to the guidelines.</li><li>I/We Author(s ) have niether given nor will give this manuscript elsewhere for publishing after submitting in STM Journal(s).</li><li>I/ We have read the original version of the manuscript and am/ are responsible for the thought contents embodied in it. The work dealt in the manuscript is my/ our own, and my/ our individual contribution to this work is significant enough to qualify for authorship.</li><li> I/We also agree to the authorship of the article in the following order:</li></ul><p>Author’s name </p><p> </p><p>1. ________________</p><p>2. ________________</p><p>3. ________________</p><p>4. ________________</p><table width="100%" border="0" cellpadding="0"><tbody><tr><td valign="top" width="5%"><p align="center"> </p></td><td valign="top" width="95%"><p>We Author(s) tick this box and would request you to consider it as our signature as we agree to the terms of this Copyright Notice, which will apply to this submission if and when it is published by this journal.</p></td></tr></tbody></table><p><strong><span style="text-decoration: underline;">Research & Reviews: Discrete Mathematical Structures </span>(RRDMS) </strong>is a journal focused towards the rapid publication of fundamental research papers on all areas of Discrete Mathematical Structures. <span>It's a triannual journal, started in 2014.</span></p><p><strong>eISSN- 2394-1979</strong></p><p><strong>Indexed In: <span>DRJI, Google Scholar</span></strong></p><p><strong><span style="text-decoration: underline;">Focus & Scope:</span></strong></p><ul><li>Mathematical induction</li><li>logic and Boolean algebra</li><li>set theory</li><li>relations and functions</li><li>sequences and series</li><li>algorithms and theory of computation</li><li>number theory</li><li>matrix theory</li><li>induction and recursion</li><li>counting and discrete probability</li><li>graph theory (trees)</li><li>Calculus of finite differences, discrete calculus or discrete analysis</li><li>Game theory, decision theory, utility theory, social choice theory</li><li>Discrete analogs of continuous mathematics</li><li>Hybrid discrete and continuous mathematics</li></ul><div><span>All contributions to the journal are rigorously refereed and are selected on the basis of quality and originality of the work. The journal publishes the most significant new research papers or any other original contribution in the form of reviews and reports on new concepts in all areas pertaining to its scope and research being done in the world, thus ensuring its scientific priority and significance.</span></div><p><a title="EDITORIAL BOARD" href="/index.php?journal=RRDMS&page=about&op=editorialTeam" target="_blank">EDITORIAL BOARD</a></p>http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2371Dirichlet Average of Hyper-geometric Kiran Function and Fractional Derivative2020-01-10T11:56:04+00:00Manoj Sharmamanoj240674@yahoo.co.inKiran Sharmamanoj240674@yahoo.co.in<p>Abstract: In this paper, first of all define a new function namely Hyper-geometric Kiran Function which is generalization of Hyper-geometric Function then a relation between Dirichlet average of Hyper-geometric Kiran function and fractional derivative is established.</p><p>Mathematics Subject Classification: 26A33, 33A30, 33A25 and 83C99.</p><p>Keywords and Phrases: Dirichlet average, Hyper-geometric Kiran function Hyper-geometric function, fractional derivative and Fractional calculus operators</p><p>Cite this Article: Manoj Sharma, Kiran Sharma. Dirichlet Average of Hyper-geometric Kiran Function and Fractional Derivative. Research & Reviews: Discrete Mathematical Structures. 2019; 6(3): 29–31p.</p>2020-01-10T11:55:39+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2351Subtract Divisor Cordial Labeling of Ring Sum of a Graphs2020-01-10T11:56:04+00:00A H Rokadahrokad86@gmail.com<p>Abstract: A subtract divisor cordial labeling of a graph G with vertex set is a bijection f from V to {1, 2,…, |V|} such that an edge is assigned the label 1 if 2 divides (f(u) – f(v)) and 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a subtract divisor cordial labeling is called a subtract divisor cordial graph. In this paper, I have Proved that ring sum of cycle with star graph, cycle with one chord with star graph, cycle with twin chords with star graph and cycle with triangle with star graphs are subtract divisor cordial graph. I also proved that ring sum of wheel with star graph, flower graph with star graph, gear graph with star graph and path graph with star graph are subtract divisor cordial graphs. Further I proved that shell graph with star graph are subtract divisor cordial graphs. And in last I proved that double fan with star graphs are subtract divisor cordial graph.</p><p>AMS Subject classification number: 05C78</p><p>Keywords: Subtract divisor cordial labeling, ring sum, shell graph, double fan, gear graph</p><p>Cite this Article: A. H. Rokad. Subtract Divisor Cordial Labeling of Ring Sum of a Graphs. Research & Reviews: Discrete Mathematical Structures. 2019; 6(3): 23–28p.</p>2020-01-10T11:49:00+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2347k-Fibonacci Polynomials in The Family of Fibonacci Numbers2020-01-10T11:56:04+00:00Engin Özkaneozkan@erzincan.edu.trMerve Taştanmervetastan24@gmail.com<p>Abstract: In this study, we define k-Fibonacci Polynomials by using terms of a new family of Fibonacci numbers given by Mikkawy and Sogabe. We compare the polynomials with known Fibonacci polynomial. Furthermore, we show the relationship between Pascal’s triangle and the coefficient of the k-Fibonacci polynomials. We give some important properties of the polynomial.</p><p>2010 Mathematics Subject Classification: 11B39.</p><p>Keywords: Fibonacci Numbers, Fibonacci Polynomials, Pascal’s triangle, k-Fibonacci polynomials, The derivative of the k-Fibonacci polynomial</p><p>Cite this Article: Engin Özkan, Merve Taştan, k-Fibonacci Polynomials in The Family of Fibonacci Numbers. Research & Reviews: Discrete Mathematical Structures. 2019; 6(3): 19–22p.</p>2020-01-10T11:44:13+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2361Generalized Yang-Fourier Transforms by using K-Function to Heat Conduction in a Semi-infinite Fractal Bar2020-01-10T11:56:04+00:00Manoj Sharmamanoj240674@yahoo.co.inKiran Sharmakiransharma2802@gmail.com<p>The main objective of present research paper to solve one-dimensional fractal heat-conduction differential equation problem in a fractal semi-infinite bar has been developed by local fractional calculus employing the analytical Generalized Yang-Fourier transforms method.</p><p><strong>Keywords</strong>: Fractal bar, heat-conduction equation, Generalized Yang-Fourier transforms, Yang-Fourier transforms, local fractional calculus, K-Function</p><p><strong>Cite this Article</strong></p><p>Manoj Sharma, Kiran Sharma. Generalized Yang-Fourier Transforms by using K-Function to Heat Conduction in a Semi-Infinite Fractal Bar. Research<em> & Reviews: Discrete Mathematical Structures</em>. 2019; 6(3): 13–18p.<strong></strong></p>2020-01-09T11:48:47+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2127Coxeter Dihedral Symmetric Tetrahedrons with Triangle Groups: Euclidean, Spherical and Hyperbolic2020-01-10T11:56:04+00:00Pranab Kalitapranabkiitg@gmail.com<p>Abstract: In this article, we have classified the Coxeter Dihedral Symmetric (CDS) tetrahedrons with triangle groups: Euclidean, Spherical and Hyperbolic. We have calculated the gram spectrums of these CDS tetrahedrons with triangle groups: Euclidean, spherical and hyperbolic, and finally studied their existence in the spaces: Euclidean, spherical and hyperbolic.</p><p>MSC 2010 Codes: 51M05, 05C50, 15A45, 15A42, 05C69.</p><p>Keywords: Coxeter Dihedral Symmetric Tetrahedrons, Triangle groups, gram matrix, spectrum, Euclidean, eigen values</p><p>Cite this Article: Pranab Kalita. Coxeter Dihedral Symmetric Tetrahedrons with Triangle Groups: Euclidean, Spherical and Hyperbolic. Research & Reviews Discrete Mathematical Structures. 2019; 6(3): 1–12p.</p>2020-01-09T10:31:18+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2019Zagreb Degree Eccentricity Indices of Graphs2020-01-09T10:27:09+00:00Padmapriya P.padmapriyap7@gmail.comVeena Mathadpadmapriyap7@gmail.com<p align="center"><strong><em>Abstract</em></strong></p><p><em>Let G be a connected graph, the first Zagreb index M<sub>1</sub>(G) of G is defined as </em><em></em><em>The second Zagreb index M<sub>2</sub>(G) of G is defined as In this paper we introduce first and second Zagreb degree eccentricity indices. Further, the first Zagreb degree eccentricity index of join, Cartesian product, tensor product, corona product of two graphs are computed.</em></p><p><em> </em></p><p><strong><em>Keywords</em></strong><em>: Zagreb indices, Eccentricity, Degree, Zagreb degree eccentricity indices.</em></p><p> </p><p><strong>Cite this Article</strong></p><p>Padmapriya P., Veena Mathad. Zagreb Degree Eccentricity Indices of Graphs. <em>Research & Reviews Discrete Mathematical Structures<strong>.</strong></em><strong> </strong><strong>2019; 6(2): 59–69p.</strong><strong></strong></p>2019-08-19T22:05:05+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2125Primitive Idempotents and Weight Distributions of Irreducible Cyclic Codes of Length 5l^m2020-01-09T10:27:09+00:00Sunil Kumarsunilklp@rediffmail.comManju Pruthisunilklp@rediffmail.comRahul .sunilklp@rediffmail.com<p align="center"><strong><em>Abstract</em></strong></p><p><em>Let </em> <em>be a finite field with q elements such that</em> <em>and </em><em>gcd </em> <em> = </em><em>1</em><em>, where</em> <em> is a prime. In this paper, we give all primitive idempotents in a ring</em> <em>[x]</em> <em>. </em><em>We give the weight distributions of all irreducible cyclic codes of length </em> <em>over</em> <em>.</em></p><p><em> </em></p><p class="Style"><strong><em>Keywords: </em></strong><em>Primitive Idempotents, Cyclotomic Cosets, Cyclic Codes.</em></p><p class="Style"> </p><p><strong>Cite this Article</strong></p><p>Sunil Kumar, Manju Pruthi, Rahul. Primitive Idempotents and Weight Distributions of Irreducible Cyclic Codes of Length . <em>Research & Reviews Discrete Mathematical Structures<strong>.</strong></em><strong> 2019; 6(2): 49–58p.</strong><strong></strong></p>2019-08-19T21:42:12+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2042On b-Coloring Parameters of Some Classes of Graphs2020-01-09T10:27:09+00:00M R Raksharakshamr94@gmail.comP Hithavarshinirakshamr94@gmail.comN K Sudevrakshamr94@gmail.comC. Dominicrakshamr94@gmail.com<p align="center"><strong><em>Abstract</em></strong></p><p><em>Vertex coloring has always been a topic of interest. Motivated by the studies on </em><em>-chromatic mean and variance of some standard graphs, in this paper, we obtain few results for </em><em>-chromatic and </em><em>-chromatic mean and variance of some cycle related graph classes. Here, Vertex coloring of a graph </em><em> is taken to be the random experiment. Discrete random variable </em><em> for this random experiment is the color of randomly chosen vertex of </em><em>. </em></p><p><strong><em>Mathematics Subject Classification</em></strong><em>: 05C15, 05C75. </em></p><p> </p><p><strong><em>Keywords</em></strong><em>: </em><em>-coloring, coloring mean, coloring variance, </em><em>-chromatic mean, </em><em>-chromatic variance.</em></p><p><strong>Cite this Article</strong></p><p>M R Raksha, P Hithavarshini, N K Sudev, C. Dominic. On -Coloring Parameters of Some Classes of Graphs. <em>Research & Reviews Discrete Mathematical Structures</em><strong><em>.</em></strong><strong> 2019; 6(2): 41–48p.</strong><strong></strong></p>2019-08-19T21:24:08+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2263Injective Coloring Parameters of Some Special Classes of Graphs2020-01-09T10:27:09+00:00V. Santhosh Priyasanthosh.priya@maths.christuniversity.inN. K. Sudevsanthosh.priya@maths.christuniversity.in<p align="center"><strong><em>Abstract</em></strong></p><p><em>The vertex coloring of a graph can be viewed as a random experiment and with respect to this experiment, a random variable </em><em> can be defined such that </em><em> denotes the color of an arbitrarily chosen vertex. In this paper, we broaden the ideas of coloring mean and variance of graphs with respect to a particular type of proper injective coloring and determine these parameters for some standard graph classes.</em></p><p><strong><em>MSC2010:</em></strong><em> 05C15, 05C38. </em></p><p><em> </em></p><p><strong><em>Keywords</em></strong><em>: Coloring mean; coloring variance; </em><em>-chromatic mean; </em><em>-chromatic variance; </em><em>-chromatic mean; </em><em>-chromatic variance. </em></p><p> </p><p><strong>Cite this Article</strong></p><p>V. Santhosh Priya, N.K. Sudev<em>.</em> Injective Coloring Parameters of Some Special Classes of Graphs.<em> Discrete Mathematical Structures</em><strong><em>.</em></strong><strong> 2019; 6(2): 30–40p.</strong><strong></strong></p>2019-08-19T04:55:29+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2128Contra Harmonic Mean Labeling for Some Tree and Corona Related Graphs2020-01-09T10:27:09+00:00J. Rajeshni Goldarajeshnigolda3@gmail.comS. S. Sandhyarajeshnigolda3@gmail.com<p align="center"><strong><em>Abstract</em></strong></p><p><em>A graph G (V,E) is called a Contra Harmonic mean graph with p vertices and q edges, if it is possible to label the vertices x</em><em>Î</em><em>V with distinct element f(x) from 0, 1,…,q in such a way that when each edge e = uv is labeled with f(e=uv) = </em><em> <!--?mso-application progid="Word.Document"?--> 16f(u)2+f(v)2f(u)+f(v)"> </em><em> or </em><em> <!--?mso-application progid="Word.Document"?--> 16f(u)2+f(v)2f(u)+f(v)"> </em><em> with distinct edge labels. The mapping f is called </em><em>Contra Harmonic </em><em>mean labeling of G.</em></p><p><em> </em></p><p><strong><em>Keywords: </em></strong><em>Graph, </em><em>Contra Harmonic mean graph, </em><em>Triangular snake, Quadrilateral snake, Step Ladder, Flower graph.</em></p><p><strong>Cite this Article</strong></p><p>J. Rajeshni Golda, S. S. Sandhya. Contra Harmonic Mean Labeling for Some Tree and Corona Related Graphs. <em>Research & Reviews Discrete Mathematical Structures</em><strong><em>.</em></strong><strong> 2019; 6(2): 24–29p.</strong><strong></strong></p>2019-08-19T04:31:17+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2124Common Fixed-Point Results for Weakly Increasing Dominating Maps on Vector b-Metric Spaces2020-01-09T10:27:09+00:00Mamta Kamramkhaneja15@gmail.comKumari Saritamkhaneja15@gmail.comRenu Chughchugh.r1@gmail.com<p align="center"><strong><em>Abstract</em></strong></p><p><em>In this paper, we consider E-b-metric space, which is a generalized vector metric space. This is a Riesz space valued metric space. Here, we prove some results concerning common fixed point for four mappings on E-b-metric space. This generalizes the results of Rahimi, Abbas and Rad [16].</em></p><p><strong><em> </em></strong></p><p><strong><em>Keywords: </em></strong><em>Dominating map, E-b-metric space, Weak annihilators, Weakly compatible, Weakly increasing</em></p><p><strong> </strong></p><p><strong>Cite this Article</strong></p><p>Mamta Kamra, Kumari Sarita, Renu Chugh. Common Fixed-Point Results for Weakly Increasing Dominating Maps on Vector b-Metric Spaces. <em>Research & Reviews Discrete Mathematical Structures<strong>.</strong></em><strong> 2019; 6(2): 7–23p.</strong><strong></strong></p>2019-08-19T04:19:55+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2132Codes Over Frobenius Groups2020-01-09T10:27:09+00:00Sudesh Sehrawatsudesh2421@yahoo.comManju Pruthisudesh2421@yahoo.com<p align="center"><strong><em>Abstract</em></strong></p><p><em>In this paper we consider the group algebra FG where G is Frobenius group </em> <em> </em><em>of order </em> <em>, where </em> <em> and char(F) does not divide order of G. We find the generating idempotents in the group algebra of Frobenius group by using character theory. We also find the minimum distance and dimension of the codes generated by these idempotents.</em></p><p class="MTDisplayEquation"><em>2010 Mathematics Subject Classification: 20G05, 20E45, 94B60</em></p><p><strong><em>Keywords: </em></strong><em>Group algebra, linear and non-linear characters,<strong> </strong>idempotents, Frobenius group.</em></p><p><em><strong>Cite this Article</strong></em></p><p><em>Sudesh Sehrawat, Manju Pruthi. Codes over Frobenius Groups. Research & Reviews Discrete Mathematical Structures<strong>.</strong> 2019; 6(2): 1–6p.</em><strong></strong></p><p><em><br /></em></p>2019-08-19T04:07:01+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2037Fractional q-Derivative and N2 Function2019-06-25T00:19:51+00:00Manoj Sharmamanoj240674@yahoo.co.inMohd. Farman Alimanoj240674@yahoo.co.in<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>The study of fractional q-calculus in this paper serves as a bridge between the fractional q-calculus in the literature and the fractional q-calculus of Special Functions. This paper is devoted to fractional q-derivative of special functions. Special functions are particular mathematical functions which have more or less established names and notations due to their importance in mathematical analysis, physics, or other applications in engineering .To begin with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit and Sharma, Jain and Ali. As a special case, of fractional q-differentiation of N<sub>2</sub> Function has been obtained.</em></p><p><strong><em>Keywords: </em></strong><em>Fractional integral and derivative operators, Fractional q-derivative, N2 Function and Special functions</em></p><p><em><strong>Mathematics Subject Classification:</strong> </em><em>Primary 33A30, Secondary 33A25, 83C99</em></p><p><em><strong>Cite this Article</strong></em></p><p>Manoj Sharma, Mohd. Farman Ali. Fractional q-Derivative and N2 Function. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1): 41–43p.</p><p><em><br /></em></p>2019-06-23T08:04:08+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2036Fractional q-Derivative and Generalized N2 Function2019-06-25T00:18:50+00:00Manoj Sharmamanoj240674@yahoo.co.inMohd. Farman Alimohdfarmanali@gmail.com<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>This paper is devoted to fractional q-derivative of special functions. To begin with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit and Sharma, Jain and Ali. As a special case, of fractional q-differentiation of N<sub>2</sub> Function has been obtained.</em></p><p><strong><em>Keywords: </em></strong><em>Fractional integral and derivative operators, Fractional q-derivative, N2 Function and Special functions</em></p><p><em><strong>Mathematics Subject Classification:</strong> </em><em>Primary 33A30, Secondary 33A25, 83C99</em></p><p><em><strong>Cite this Article</strong></em></p><p>Manoj Sharma, Mohd. Farman Ali. Fractional Q-Derivative and Generalized N2 Function. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1): 38–40p.</p><p><em><br /></em></p>2019-06-23T08:04:02+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2043FRACTIONAL q-DERIVATIVE AND GENERALIZED K-FUNCTION2019-06-25T00:18:51+00:00Manoj Sharmamanoj240674@yahoo.co.inLaxmimorya .laxmimorya91@gmail.comRajshree Mishrarajshreemishraa@gmail.com<p align="center"><strong><em>Abstract</em></strong><em></em></p><p><em>This investigation is basically intended to fractional q-derivative of special functions. In this article we drive the results on term by term q-fractional differentiation of a generalized k-Series. As particular case we will obtain the fractional q-differentiation of the power series and exponential series. To start with the theorem on term by term q-fractional differentiation has been derived. The result is an extension of an earlier result due to Yadav and Purohit (2004) and Sharma, Jain and Ali (2009). As a special case, of fractional q-differentiation of generalized K-series has been obtained.</em></p><p><strong><em> </em></strong><em><strong>Mathematics Subject Classification—</strong></em><em>Primary 33A30, Secondary 33A25, 83C99</em></p><p><em> </em><strong><em>Keywords: </em></strong><em>Fractional integral and derivative operators, fractional q-derivative, generalized K-series and special functions</em></p><p><strong>Cite this Article</strong></p><p>Manoj Sharma, Laxmimorya, Rajshree Mishra. Fractional q-Derivative and Generalized K-Function. <em>Research & Reviews: Discrete Mathematical Structures.</em> 2019; 6(1): 6–9p.<strong></strong></p><p><em><br /></em></p>2019-05-17T00:01:27+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1997On Generalized fractional Integral Operators2019-06-25T00:18:51+00:00T. G. Thangetgthange@gmail.com<h4><em>Abstract</em></h4><p><em>In this paper, different integral operators for functions of two variables namely fractional</em><em> integral operator and generalized fractional integral operator</em><em> have been defined</em><em>. Also defined the different spaces for functions of two variables and</em><em> studied defined the operators on these spaces. Finally, proved the</em><em> generalized fractional integral operators for function of two variables that are </em><em>bounded from a generalized Morrey space of functions of two variables to another.</em></p><p><strong>Keywords</strong>: fractional integral operator, function space, generalized fractional integral operator, Morrey spaces.</p><p><strong>Cite this Article</strong></p><p>T.G. Thange. On Generalized Fractional Integral Operators. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1): 10–14p.<strong></strong></p>2019-05-16T23:51:53+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1996Resolving Travelling Salesman Problem Using Modified Clustering Technique2019-06-25T00:18:50+00:00Hardik Dhingradhingrahardik1997@gmail.comGagan Deep Dhandgdgagan696@gmail.comRashmi Chawlarashmichawlaymca@gmail.comShailender Guptashailender81@gmail.comSamarth Mittalsamarthmittal1498@gmail.com<p align="center"><strong><em>Abstract</em></strong></p><p><em>Travelling Salesman Problem (TSP) is a quotidian stumbling block in the field of Computer Science and operation research designed to seek out the shortest pathway amid the given targets viz. cities where each target is considered only once. Many solutions to this setback like Ant Colony Optimization. Brute-Force approach, Genetic Algorithm, Fruit Fly Optimization etc. are available in literature. The main objective of these solutions is to minimize the time complexity and to search an optimized path that covers the entire region; however the urge of finding shortest path in minimum time still persists. This research work is an attempt to solve the above problem using clustering technique. Generally, for N cities the number of permutations conventionally considered are (N-1); for the proposed research work the permutations contemplated are reduced by the factor m. The results exhibit that the proposed method can effectively improve time complexity and search ability for achieving higher accuracy and optimal results. TSP discerns its application in X-Ray crystallography, the order-picking problem in warehouses, drilling of Printed Circuit Boards (PCB), mission planning problem etc. so an exigency for an optimum solution is requisite.</em></p><p><strong><em>Keywords: </em></strong><em>Brute-Force, lexicographic ordering, non-deterministic polynomial (NP) hard problem</em></p><p><strong>Cite this Article</strong></p><p>Hardik Dhingra, Gagan Deep Dhand, Rashmi Chawla, Shailende Gupta, Samarth Mittal. Resolving Travelling Salesman Problem Using Modified Clustering Technique. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1):<br /> 22–31p.<strong></strong></p><p><em><br /></em></p>2019-05-16T22:17:49+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1995n-Dimensional Eigenfunction Wavelet Transform2019-06-25T00:18:50+00:00T. G. Thangetgthange@gmail.comR. D. Swamitgthange@gmail.comA. M. Aluretgthange@gmail.com<h4><em>Abstract</em></h4><p><em>In this paper, Eigenfunction transform defined for single variable is extended for functions of n variables. Translation, convolution and dilation associated with n dimensional Eigenfunction transform are defined. Also, we define Eigenfunction wavelet for n variables. Eigenfunction wavelet transform (EWT) for n variables is introduced. Inversion formula for n dimensional EWT is also derived. </em></p><p><strong>Keywords:</strong> Eigenfunction transform Eigenfunction wavelet transform, translation, convolution, dilation</p><p><strong>Cite this Article</strong></p><p>T.G. Thange, R.D. Swami, A.M.Alure. n-Dimensional Eigenfunction Wavelet Transform. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1):<br /> 32–37p.</p>2019-05-16T22:01:52+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1939Commutativity of Some Graph Operators2019-06-25T00:18:50+00:00Jeepamol J Palathingaljeepamoljp@gmail.comAparna Lakshmanan Saparnaren@gmail.com<p align="center"><strong><em>Abstract</em></strong></p><p><em>The line graph L(G) of a graph G has the edges of G as its vertices and two distinct edges of G are adjacent in L(G) if they are incident in G. In this paper we consider the commutativity of the line graph operator with some other operators such as Gallai graph Γ(G), anti- Gallai graph Δ(G), k<sup>th</sup> power of a graph Pow<sub>k</sub>(G), k-distance graph T<sub>k</sub>(G), cycle graph C<sub>y</sub>(G), block graph B(G), subdivision graph S(G), total graph T(G) and middle graph Mid(G).</em></p><p><strong><em>Keywords:</em></strong><strong> </strong><em>Line graph, graph operators, commutativity</em></p><p><strong>Cite this Article</strong></p><p>Jeepamol J. Palathingal, Aparna Lakshmanan S. Commutativity of Some Graph Operators. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1): 1–5p.</p><p><em><br /></em></p>2019-05-16T21:53:12+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1900On the Pendant Number of Some New Graph Classes2019-06-25T00:18:50+00:00Jomon K Sebastianjomoncmi@gmail.comJoseph Varghese Kureetharafrjoseph@christuniversity.inSudev Naduvathsudev.nk@christuniversity.inCharles Dominiccharles.dominic@christuniversity.in<p align="center"><strong><em>Abstract</em></strong></p><p><em>A decomposition of a graph </em><em> is a collection of its edge disjoint sub-graphs such that their union is </em><em>. If all the sub-graphs in the decomposition are paths, then it is a path decomposition. In this paper, we discuss the pendant number, the minimum number of end vertices of paths in a path decomposition of a graph. We also determine this parameter for some graph classes.</em></p><p><strong><em>Keywords: </em></strong><em>Decomposition, path decomposition, pendant number</em>.</p><p><strong>MSC2010: </strong>05C70, 05C38, 05C40</p><p><strong>Cite this Article</strong></p><p>Jomon K. Sebastian, Joseph Varghese Kureethara, Sudev Naduvath, Charles Dominic. On the Pendant Number of Some New Graph Classes. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2019; 6(1): 15–21p.<strong></strong></p>2019-05-03T04:04:35+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1870Use of Matlab in Teaching The Fundamentals of Probability2019-02-07T03:10:04+00:00Bhavika M Patelbhavika0612@gmail.comTruptiben A Desaibhavika0612@gmail.com<p align="center">The aim of this paper is to improve teaching efficiency with use of powerful educational software called 'MATLAB'. In this paper using the 'MATLAB' tool 'Makeshow' we attractively introduce normal probability distribution for the normally distributed random variables. Using these tool students can easily create interactive slideshows. Because of their rich library, available tools and demos matlab is easy to use for the students and so it provides option of self-study tool for them. This type of educational software allows the students to establish relationship between the problems solved in classroom and the reality that these problems refer to.<strong><em> </em></strong></p><p><strong>Cite this Article</strong></p><p>Bhavika M. Patel, Truptiben A. Desai. Use of Matlab in Teaching the Fundamentals of Probability. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3):<br /> 31–35p.<strong></strong></p><p align="center"><strong><em><br /></em></strong></p>2019-02-07T02:21:10+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1868Degree and Distance in 2-cartesian Product of Graphs2019-02-07T03:06:57+00:00H.S. Mehtamatha.urvashi@adit.ac.inU. P. Acharyamatha.urvashi@adit.ac.in<p class="CM17" align="center"><em>The cartesian product of two graphs is well-known graph product and studied in detail. This concept has been generalized by introducing 2-cartesian product of graphs. The connectedness of 2-cartesian product of graphs has been discussed earlier. In this paper, ﬁrst we obtain degree formula and discuss regularity of this product of graphs. Also, we have discuss distance between two vertices in this product.</em></p><p><strong>Cite this Article</strong></p><p>H.S. Mehta and U.P. Acharya. Degree and Distance in 2-Cartesian Product of Graphs. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3): 11–14p.</p>2019-02-07T02:21:05+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1865Solution of Solid Traveling Purchaser Problem Using Eﬃcient Genetic Algorithm with Probabilistic Selection and Multi-Parent Crossover Technique2019-02-07T03:02:16+00:00Arindam Royroyarindamroy@yahoo.com<p>In this paper, I design a NP-hard optimization problem and solve this problem by developing a nature-based multi-parent crossover in genetic algorithm (GA). Initially, taking a set of markets, a depot and some products for each of which a positive demand is specified. Purchaser can purchase each product from a subset of markets only a given quantity, less than or equal to the required one, can be purchased at a given unit price. Traveling purchaser forms a cycle starting at and ending to the depot and visiting a subset of markets at a minimum traveling cost. Here, I consider multiple vehicle to visit different markets say solid TPP (STPP). The activeness of my model is illustrated by numerical examples.</p><p><strong>Cite this Article</strong></p><p>Arindam Roy. Solution of Solid Traveling Purchaser Problem Using Efficient Genetic Algorithm with Probabilistic Selection and Multi-Parent Crossover Technique. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3):<br /> 20–26p.</p>2019-02-07T02:21:01+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1833Characterization of topologically 1-uniform dcsl graphs and learning graphs2019-02-07T02:56:24+00:00Germina K. Augusthysrgerminaka@gmail.comGency Josephsranjosh@gmail.comL Benedict Michael RAjbenedict.mraj@gmail.com<p>A distance compatible set labeling (dcsl) of a connected graph $G$ is an injective set assignment $f : V(G) \rightarrow 2^{X},$ $X$ being a non empty ground set, such that the corresponding induced function $f^{\oplus} :E(G) \rightarrow 2^{X}\setminus \{\phi\}$ given by $f^{\oplus}(uv)= f(u)\oplus f(v)$ satisfies $ |f^{\oplus}(uv)| = k_{(u,v)}^{f}d_{G}(u,v) $ for every pair of distinct vertices $u, v \in V(G),$ where $d_{G}(u,v)$ denotes the path distance between $u$ and $v$ and $k_{(u,v)}^{f}$ is a constant, not necessarily an integer, depending on the pair of vertices $u,v$ chosen. A dcsl $f$ of $G$ is $k$-uniform if all the constants of proportionality with respect to $f$ are equal to $k,$ and if $G$ admits such a dcsl then $G$ is called a $k$-uniform dcsl graph. Let $\mathcal{F}$ be a family of subsets of a set $X.$ A graph $G$ is defined to be a learning graph, if it is a ${\mathcal{F}}$-induced graph of some learning space ${\mathcal{F}}.$ A graph $G$ is called a topologically $k$-uniform dcsl graph, if $\{f(V(G)\}$, the collection of vertex labeling of $G$ is a topology. In this paper, we characterize topologically $1$-uniform dcsl learning graphs.</p><p><strong>Cite this Article</strong></p><p>Gency Joseph, L. Benedict Michael Raj, Germina K. Augusthy. Characterization of Topologically 1-Uniform DCSL Graphs and Learning Graphs. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3): 6–10p.</p>2019-02-07T02:14:56+00:00http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1854Control Chart for Attributes based on Inverse Rayleigh Distribution2019-02-07T02:52:32+00:00K. Kowsalyakowsalyastat1993@gmail.comK. Sathish Kumarkowsalyastat1993@gmail.comK. Arulkowsalyastat1993@gmail.com<p>In this paper, a new attribute control chart based on inverse Rayleigh distribution is developed under a time truncated life test. The number of failures is observed from the life test and the fraction nonconforming is to be monitored by two pairs of lower and upper control limits. The simulation study shows the efficiency of the developed chart. An example is provided for illustrating the new control chart.</p><p><strong>Cite this Article</strong></p><p>Kowsalya K, Sathish Kumar K, Arul K. Control Chart for Attributes based on Inverse Rayleigh Distribution. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3): 1–5p.</p>2019-02-07T02:14:51+00:00