Research & Reviews: Discrete Mathematical Structures
http://computers.stmjournals.com/index.php?journal=RRDMS
<p><strong><span style="text-decoration: underline;">Research & Reviews: Discrete Mathematical Structures </span>(RRDMS) </strong>is a print and e-journal focused towards the rapid publication of fundamental research papers on all areas of Discrete Mathematical Structures.</p><p>Discrete mathematical structures journal deals with discrete objects. Discrete objects are those which are separated from each other like integers, rational numbers, automobiles, houses, peoples etc. are all discrete objects. Some of the major reasons that we adopt Discrete mathematics are. We can handle infinity or large quantity and indefiniteness with them which results from formal approaches are reusable.</p><p>eISSN- 2394-1979</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 analogues of continuous mathematics</li><li>Hybrid discrete and continuous mathematics</li></ul>en-US<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>sugandha.mishra@celnet.in (Sugandha Mishra)info@stmjournals.com (Administrator)Fri, 03 May 2019 04:04:56 -0700OJS 2.4.2.0http://blogs.law.harvard.edu/tech/rss60FRACTIONAL q-DERIVATIVE AND GENERALIZED K-FUNCTION
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2043
<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>Manoj Sharma, Laxmimorya ., Rajshree Mishrahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=2043Fri, 17 May 2019 00:01:27 -0700On Generalized fractional Integral Operators
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1997
<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>T. G. Thangehttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1997Thu, 16 May 2019 23:51:53 -0700Resolving Travelling Salesman Problem Using Modified Clustering Technique
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1996
<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>Hardik Dhingra, Gagan Deep Dhand, Rashmi Chawla, Shailender Gupta, Samarth Mittalhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1996Thu, 16 May 2019 22:17:49 -0700n-Dimensional Eigenfunction Wavelet Transform
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1995
<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>T. G. Thange, R. D. Swami, A. M. Alurehttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1995Thu, 16 May 2019 22:01:52 -0700Commutativity of Some Graph Operators
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1939
<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>Jeepamol J Palathingal, Aparna Lakshmanan Shttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1939Thu, 16 May 2019 21:53:12 -0700On the Pendant Number of Some Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1900
A decomposition of a graph G is a collection of its edge-disjoint sub-graphs such that their union is G. 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.Jomon K Sebastian, Joseph Varghese Kureethara, Sudev Naduvath, Charles Dominichttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1900Fri, 03 May 2019 04:04:35 -0700Use of Matlab in Teaching The Fundamentals of Probability
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1870
<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>Bhavika M Patel, Truptiben A Desaihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1870Thu, 07 Feb 2019 02:21:10 -0700Degree and Distance in 2-cartesian Product of Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1868
<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>H.S. Mehta, U. P. Acharyahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1868Thu, 07 Feb 2019 02:21:05 -0700Solution of Solid Traveling Purchaser Problem Using Eﬃcient Genetic Algorithm with Probabilistic Selection and Multi-Parent Crossover Technique
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1865
<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>Arindam Royhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1865Thu, 07 Feb 2019 02:21:01 -0700Characterization of topologically 1-uniform dcsl graphs and learning graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1833
<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>Germina K. Augusthy, Gency Joseph, L Benedict Michael RAjhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1833Thu, 07 Feb 2019 02:14:56 -0700Control Chart for Attributes based on Inverse Rayleigh Distribution
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1854
<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>K. Kowsalya, K. Sathish Kumar, K. Arulhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1854Thu, 07 Feb 2019 02:14:51 -0700Production Inventory Model for Deteriorating Products with Lifetime
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1867
<p>In this paper, an inventory model has been developed with production proportional to quadratic demand during life time and linear demand is taken during deterioration period. The deterioration rate is taken of power pattern form, i.e. 14 Î±Î²tÎ²-1"> . Shortage is not allowed.</p><p><strong>Cite this Article</strong></p><p>Rajender Kumar, Manju Pruthi, Gulshan Taneja. Production Inventory Model for Deteriorating Products with Lifetime. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3):<br /> 15–19p.</p>Rajender Kumar, Manju Pruthi, Gulshan Tanejahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1867Fri, 25 Jan 2019 04:37:37 -0700Some Algebraic Properties of me-homomorphism of Semi graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1936
<p>The theory of Semi graph was introduced by E. Sampat Kumar [6] which is analogous with theory of Hyper graph. Study of Homomorphism[4] is useful to prove numerous application of Graph theory, which is adjacency preserving mapping. In this Paper we have introduced me-homomorphism of Semi graphs and derived some of its algebraic properties [5]. We have also investigated nature of some parameters and its bounds under this mapping.</p><p><strong>Cite this Article</strong></p><p>P.D. Uchat, M.S. Sutaria. Some Algebraic Properties of me-homomorphism of Semi-Graphs. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2018; 5(3):<br /> 27–30p.</p>Paras Dineshchandra Uchat, Maitri Sutariahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1936Wed, 23 Jan 2019 23:45:50 -0700A Graph Theoretic Approach to quantify the Conflict of Traffic Streams in a Traffic Intersection
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1538
<p>A traffic intersection can be modelled by a graph by considering the streams as vertices and assigning an edge based on the mutually non-conflict streams. In this paper we propose a spectral approach to arrange the steams in order of their conflict and hence determine the most conflicted stream in a traffic intersection.<strong> </strong></p>Ankur Bharalihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1538Fri, 21 Sep 2018 02:06:29 -0700FD and DDA of N2 Function
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1695
<p>The object of the present paper is to establish the results of Double Dirichlet average (DDA) of N<sub>2</sub> Function, using Riemann-Liouville Fractional derivative (FD). This function is a modified form of Mittag-Leffler function [15]. The author drives the results between N2-function and fractional operators. The N<sub>2 </sub>Function can be measured as a Dirichlet average and connected with fractional calculus. In this paper the solution comes in compact form of double Dirichlet average of N<sub>2 </sub>Function.</p>Mohd. Farman Ali, Manoj Sharmahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1695Fri, 21 Sep 2018 01:59:46 -0700Further Results on Some Degree Based Topological Indices of Sierpi´cski Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1486
Sierpi´cski graphs S(n, k) were defined originally in 1997 by Sandi Klavˇzar<br />and Uroˇs Milutinovi´c. In this paper, degree based topological indices of<br />Sierpi´cski graphs are considered. In particular M1(G), M2(G), M1(G, x), M2(G, x), R(G), (G), ABC(G), ABC4(G), GA(G), GA5(G), H(G), AZI(G), S(G) and F(G) of Sierpi´cski graphs are determined.Padmapriya Phttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1486Fri, 21 Sep 2018 01:37:17 -0700On Structure and Robustness of Airport Network of India
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1468
This paper uses a complex network approach to study the structure and robustness of Airport Network of India (ANI). The ANI displays small-world (SW) network properties with an average path length of 2.262 and a clustering coefficient of 0.605, and it also exhibits disassortative mixing on degree of nodes, that means the high-degree nodes in the network tend to have connections with low-degree nodes. Being a disassortative network, ANI doesn’t percolate more easily and less robust to node removal. A study of the robustness of ANI is also carried out for targeted node removal.Ankur Bharali, Dimpee Baruahhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1468Sat, 01 Sep 2018 10:30:58 -0700Vertex Odd Divisor Cordial Labeling of Ring Sum of Different Graphs With star Graph
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1696
<p>A graph <em>tt </em>= (<em>V,</em><em> </em><em>E</em>) is said to have a vertex odd divisor cordial labeling if there is a bijection <em>f </em>: <em>{</em>1<em>, </em>3<em>, </em><em>. . . , </em>2<em>n </em><em>− </em>1<em>} </em>such that each edge <em>e </em>= <em>uv </em>is assigned the label 1 if <em>f </em>(<em>u</em>)<em>|</em><em>f </em>(<em>v</em>) or <em>f </em>(<em>v</em>)<em>|</em><em>f </em>(<em>u</em>) and 0 otherwise, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. If a graph admits a vertex odd divisor cordial labeling, then it is called vertex odd divisor cordial graph. In this paper we have derived vertex odd divisor cordial labeling of ring sum of different graphs.</p>D. G. Adalja, G. V. Ghodasarahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1696Fri, 31 Aug 2018 03:36:36 -0700Difference Cordial Labeling in context of Joint sum of Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1570
<p>Suppose G be a (p, q) graph. Suppose f be a map from f(G) to {1,2,...,p}. For each edge xy assign, the label |f(x) – f(y)|. f is difference cordial if f is 1-1 and |e<sub>f</sub>(0) – e<sub>f</sub>(1)| <!--?mso-application progid="Word.Document"?--> 14â‰¤"> 1, where e<sub>f</sub>(1) and e<sub>f</sub>(0) denote the number of edges with labeled 1 except labeled with 1 respectively. A graph which admit difference cordial labeling is called a difference cordial graph.</p><p> In this paper I prove the following results.</p><ol><li>The joint sum of two copies of wheel graph is difference cordial.</li><li>The joint sum of two copies of shell graph is difference cordial.</li><li>The joint sum of two copies of double wheel graph is difference cordial.</li><li>The joint sum of two copies of Petersen graph is difference cordial.</li><li>The joint sum of two copies of coconut tree is difference cordial.</li></ol>amit himmatbhai rokadhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1570Tue, 26 Jun 2018 23:40:43 -0700E-Cordial Labeling for Theta Graph
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1463
<strong><em> </em></strong>A binary vertex labeling <em>f </em>:<em> E</em>(<em>G</em>)<em> → </em>{0,1} with induced labeling <em>f <sup>* </sup></em>:<em> V</em>(<em>G</em>)<em> → </em>{0,1} defined by <em>f <sup>*</sup></em>(<em>v</em>) = ∑ { <em>f </em>(<em>uv</em>) : <em>uv </em>ϵ <em>E</em>(<em>G</em>)}(<em>mod 2</em>) is called an E-cordial labeling of graph <em>G</em> if the number of vertices labeled 0 and number of vertices labeled 1 differ by at most 1and the number of edges labeled 0 and number of edges labeled 1 differ by at most 1. A graph which admits E-cordial labeling is called an E-cordial graph. We prove that the graphs obtained by duplication, switching, fusion and open star of theta graph <em>T<sub>α</sub></em> are E-cordial graphs.vishnu prakashhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1463Sun, 24 Jun 2018 22:38:39 -0700Analysis of Numerical and Categorical Prediction Algorithms : A Case Study of Hypertension
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1558
<strong>An extremely wide variety and volume of data are generated by the healthcare industries which can be effectively utilized by applying data mining techniques so as to attain significant knowledge that can aid the process of decision making. In this paper an analysis of Prediction Algorithms is performed using clinical data of hypertension patients. Data mining techniques are effectively employed to estimate systolic and diastolic blood pressure of patients and categorize the risk level for each patient.</strong>Ashwini Menonhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1558Tue, 19 Jun 2018 23:29:49 -0700Chromatic Curling Number of Certain Derived Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1229
<p>The curling number of a graph G is dened as the number of times an element in the degree sequence of G appears the maximum number of times. Graph colouring is an assignment of colours, labels or weights to the vertices or edges of a graph. A colouring C of colours c1, c2,..., cl is said to be a minimum parameter colouring if C consists of minimum number of colours with smallest subscripts. In this paper, we study the chromatic colouring version of curling number of certain derived graphs, with respect to their minimum parameter colourings.</p>Susanth Chandoor, Sudev Naduvath, Sunny Joseph Kalayathankalhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1229Mon, 28 May 2018 04:40:27 -0700Fibonacci Cordial Labeling of Some Graphs
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1416
<p><em>An injective function f: V (G) → {F0, F1, F2, . . . , Fn+1}, where Fj is the j<sup>th</sup> Fibonacci number (j = 0, 1, . . . , n+1), is said to be Fibonacci cordial labeling if the induced function f </em><em>∗</em><em> </em><em>: E(G) → {0, 1} defined by f </em><em>∗</em><em>(uv)</em><em> </em><em>= (f (u) + f (v))(mod2) satisfies the condition |e<sub>f </sub>(0) − e<sub>f</sub> (1)| ≤ 1. A graph which admits Fibonacci cordial labeling is called Fibonacci cordial graph. In this paper, the author investigated the existence of Fibonacci Cordial Labeling of some Graphs.<strong></strong></em></p>amit himmatbhai rokadhttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1416Mon, 09 Apr 2018 21:27:20 -0700INTEGRAL REPRESENTATION OF K-FUNCTION
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1266
<p><strong>Abstract: </strong>In this article, an attempt to be made to introduce the four-different integral representation of Extended K-function and special cases have also been discussed [1, 2]. The Extended K Function which is introduced by the authors first time in this work is extended version of earlier K-Function of Sharma [3]. We will use Riemann-Liouville fractional calculus operator in finding the integral representation of this extended K- Function. Fractional Calculus operators means calculus operators of arbitrary order (real, complex), So, these operators are useful in finding Integral representations of special functions of fractional calculus.</p><p><strong>Mathematics Subject Classification</strong>: 33C60, 33E12, 82C31, 26A33 </p><p><strong>Keywords</strong>: Riemann-Liouville fractional derivative operator, K-function, Gamma and Beta Function, M-Function.</p><p><strong>Cite this Article</strong></p><p><span style="font-size: medium;">Manoj Sharma, Laxmi Morya, Rajshree Mishra. Integral Representation of K-Function</span><span style="font-size: medium;">. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3):<br /> 81–88p.</span></p>Manoj Sharma, Laxmi Morya, Rajshree Mishrahttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1266Mon, 22 Jan 2018 03:42:03 -0700Advanced Computable Extension of New Fractional Kinetic Equation
http://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1265
<p class="Standard" align="center"><strong><em>Abstract</em></strong><strong><em></em></strong></p><p class="Standard"><em>The aim of this work is to find</em><em> advanced computable extension of kinetic equation with fractional calculus approach. Fractional calculus originated in 1695, shortly after the inversion of classical calculus. The pioneer researchers who studied it were Liouville, Riemann, Leibniz, etc. For a long time, fractional calculus has been regarded as a pure mathematical area without applications. But, in recent decades, such type of synergism has been changed. It has been found that fractional calculus can be useful and even a powerful tool and a précis of the simple information about fractional calculus and its applications can be found in literature. The first use of a derivative of non-integer order is credited to the French mathematician S. F. Lacroix in 1819 who expressed the derivative of non-integer order </em> <em>in terms of Legendre’s factorial symbol </em><em>G</em><em>.</em></p><p><strong><em>Mathematics Subject Classification: </em></strong><em>33C60, 33E12, 82C31, 26A33.</em></p><p><strong><em>Keywords: </em></strong><em>Fractional kinetic equation, </em><em>new modified generalized </em> <em>function</em><em>, Riemann-Liouville operator, Laplace transform</em><em>, modified Riemann-Liouville fractional derivative operator, differential equation</em></p><p><strong>Cite this Article</strong></p><p><span style="font-size: medium;">Sharma M, Tyagi A. Advanced Computable Extension of New Fractional Kinetic Equation. <em>Research & Reviews: Discrete Mathematical Structures</em>. 2017; 4(3): 74–80p.</span></p><p><em><br /></em></p>Manoj Sharma, A. Tyagihttp://computers.stmjournals.com/index.php?journal=RRDMS&page=article&op=view&path%5B%5D=1265Mon, 22 Jan 2018 03:36:10 -0700