Research Article
Article:(k,r) - Semi Strong Chromatic Number of a Graph
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
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| Volume 21 - Issue 2 |
| Published: May 2011 |
| Authors: G. Jothilakshmi, A. P. Pushpalatha, S.Suganthi, V.Swaminathan |
10.5120/2486-3354
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G. Jothilakshmi, A. P. Pushpalatha, S.Suganthi, V.Swaminathan . Article:(k,r) - Semi Strong Chromatic Number of a Graph. International Journal of Computer Applications. 21, 2 (May 2011), 7-10. DOI=10.5120/2486-3354
@article{ 10.5120/2486-3354,
author = { G. Jothilakshmi,A. P. Pushpalatha,S.Suganthi,V.Swaminathan },
title = { Article:(k,r) - Semi Strong Chromatic Number of a Graph },
journal = { International Journal of Computer Applications },
year = { 2011 },
volume = { 21 },
number = { 2 },
pages = { 7-10 },
doi = { 10.5120/2486-3354 },
publisher = { Foundation of Computer Science (FCS), NY, USA }
}
%0 Journal Article
%D 2011
%A G. Jothilakshmi
%A A. P. Pushpalatha
%A S.Suganthi
%A V.Swaminathan
%T Article:(k,r) - Semi Strong Chromatic Number of a Graph%T
%J International Journal of Computer Applications
%V 21
%N 2
%P 7-10
%R 10.5120/2486-3354
%I Foundation of Computer Science (FCS), NY, USA
Abstract
Let G = (V,E) be a simple, finite, undirected graph. Let k, r be positive integers. A set S V (G). A partition of V(G) is called (k,r) - semi strongly stable set if |Nr (u) S| ≤ k, for all u Є V(G). A partition of V(G) into (k, r) - semi strongly stable sets is called (k, r) - semi strong coloring of G. The minimum order of a (k, r) - semi strong coloring of G is called (k, r) - semi strong chromatic number of G and it is denoted by Xs(k,r)(G). The number Xs(k,r)(G) is determined for various known graphs and some bounds are obtained for it.
References
- J. A. Andrews and M. S. Jacobsn, On a generalization of chromatic number, Congr. Numer. 47(1985) 33-48
- G. Chartrand, D. Geller and S. Hedetniemi, A generalization of chromatic number, Proc. Cambridge Philos. Soc64(1968) 265-271.
- Florica Kramer and Horst Kramer, A survery on the distance-colouring of graphs, presented in the International confrernce Combinatorics’04, Capomulini (Catania, Italy).
- F. Harary, Graph Theory (Addison- Wesley, Reading, MA, 1969).
- EA Nordhaus, JW Gaddum, On complementary graphs, AM. Math. Monthly 63 (1956) 175-177.
- E.Sampthkumar, Generalizations of independence and chromatic numbers of a graph, Discrete Math. 115(1993) 245-251.
- E.Sampathkumar amd G.D.Kamath,k-size Chromatic number of a graph,The Indian Journal of statistics, Special Volume 54(1992) 393-397.
- E. Sampthkumar and P. S. Neeralagi and C. V. Venkatachalam, A generalization of chromatic and line chromatic number, J. Karnatak Univ, Sci. 22(1977) 44-49.
- E. Sampthkumar and C. V. Venkatachalam, Chromatic partitions of a graph, Discrete Math. 74(1989) 227-239.
- Timothy J. Bean, Michael A. Henning, Henda C. Swart, On the integrity of distance domination in graphs,Australian Journal of Combinatorics, 10(1994) 29-43.
- A. Toft, On critical subgraphs of color-critical graphs, Discrete Math. 7(1974) 377-392.
- Doughlas B. West, Intoduction to Graph Theory (Prentice- Hall of India, 2003).
- E.Sampathkumar, L. Pushpalatha, Semi strong chromatic number of a grpah, Indian J. Pure appl Math., 26(1) : 35-40, January 1995.
- G.Jothilakshmi, A. P. Pushpalatha, S. Sugnathi and V. Swaminathan, (k,r)-coloring, International Journal of Mathematics, Computer Science and Information Technology, Vol. 1, December 2008. pp 211-219.
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