Chromatic Curling Number of Certain Derived Graphs
DOI:
https://doi.org/10.37591/rrdms.v5i1.1229Keywords:
Graph colouring, curling number, compound curling number, chro- matic curling number, chromatic compound curling number.Abstract
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.
References
J.A. Bondy and U.S.R. Murty, Graph theory, (Springer, New York, 2008).
G. Chartrand and P. Zhang, Chromatic graph theory, (CRC Press, Boca Raton,
.
B. Chan, J. P. Linderman, N. J. A. Sloane, A. R. Wilks, On curling numbers
of integer sequences, J. Integer Seq., 16(2013), Article-13.4.3, 1-31.
B. Chan, N. J. A. Sloane, The curling number conjecture, Preprint,
arXiv:0912.2382v5 [math.CO].
K.P. Chithra, E.A. Shiny and N.K. Sudev, On colouring parameters of certain
cycle related graphs, Contemp. Stud. Discrete Math., 1(1)(2017), 1{10.
K.P. Chithra, N.K. Sudev, S. Satheesh, K.A. Germina and J. Kok, On cer-
tain colouring parameters of Mycielski graphs of some graphs, Discrete Math.
Algorithm Appl., (2017), to appear.
F. Fornasiero and S. Naduvath, On J-colourability of certain derived graph
classes, communicated.
F. Harary, Graph theory, (Narosa Publ., New Delhi, 2001).
T.R. Jensen and B. Toft, Graph colouring problems, (John Wiley & Sons, 1995).
M. Kubale, Graph colourings, (American Mathematical Society, 2004).
J. Kok, N.K. Sudev, and U. Mary, On chromatic Zagreb indices of certain
graphs, Discrete Math. Algorithm. Appl., 09(1)(2017), 1750014:1-14, DOI:
1142/S1793830917500148.
J. Kok, N. K. Sudev, K. P. Chithra, On curling number of certain graphs,
Southeast Asian Bull. Math., (2017), in press.
W. Lin, J. Wu, P. C. B. Lam, G. Gu, Several parameters of gen-
eralized Mycielskians, Discrete Appl. Math., 154(8)(2006), 1173-1182,
DOI:10.1016/j.dam.2005.11.001.
W. Meyer, Chromatic colouring, Amer. Math. Monthly, 80(1973), 920{922.
N.K. Sudev, K.P. Chithra, S. Satheesh and J. Kok, On certain parameters
of equitable colouring of graphs, Discrete Math. Algorithm Appl., 9(4)(2017),
{11., DOI: 10.1142/S1793830917500549.
N.K. Sudev, Some new results on equitable coloring parameters of graphs,
communicated.
N.K. Sudev, On the curling number of the Mycielskian of certain graphs, J.
Combin. Math. Combin. Comput, to appear.
N. Sudev, C. Susanth, K. Chithra, J. Kok and S.J. Kalayathankal, Some new
results on the curling number of graphs, J. Combin. Math. Combin. Comput,
to appear.
C. Susanth, S.J. Kalayathankal, N.K. Sudev, K.P. Chithra and J. Kok, Curling
number of certain graph classes, J. Combin. Math. Combin. Comput, to appear.
C. Susanth, S.J. Kalayathankal, N.K. Sudev, K.P. Chithra and J. Kok, Curling
number of certain graph powers, preprint, arXiv:1509.00220 [math.GM]
D.B. West, Introduction to graph theory, (Pearson Education Inc., Delhi 2001).
Downloads
Published
Issue
Section
License
Declaration and Copyright Transfer Form
(to be completed by authors)
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 not published already in part or whole (except in the form of abstract) in any journal or magazine for private or public circulation, and, is not under consideration of publication elsewhere.
- 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.
- I/We Author(s ) have niether given nor will give this manuscript elsewhere for publishing after submitting in STM Journal(s).
- 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.
- I/We also agree to the authorship of the article in the following order:
Author’s name
1. ________________
2. ________________
3. ________________
4. ________________
| 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. |