SOME RESULTS ON THE DISTANCE r-b-COLORING IN GRAPHS
Year 2016,
Volume: 6 Issue: 2, 315 - 323, 01.12.2016
G. Jothilakshmi
A. P. Pushpalatha
S. Suganthi
V. Swaminathan
Abstract
Given a positive integer r, two vertices u; v 2 V G are r- independent if d u; v > r. A partition of V G into r-independent sets is called a distance r-coloring. A study of distance r-coloring and distance r-b-coloring concepts are studied in this paper.
References
- R.Balakrishnan, S.Francis Raj and T.Kavaskar, Coloring the Mycielskian, Proceeding of International Conference -ICDM (2008), 53-57.
- G.Chartrand, D.Geller and S.Hedetniemi, A generalization of chromatic number, Proc. Cambridge Philos. Soc. 64 (1968), 265-271.
- M.Chundovsky and P.D.Seymour,The structure of claw-free graphs, manuscript 2004.
- Douglas B.West, Introduction to Graph Theory (Prentice-Hall of India), 2003.
- M.A.Henning, Distance Domination in Graphs:, Advance Topics(Eds:Teresa W. Haynes, Stephen T. Hedetniemi, Peter J. Slater), 321-349, Marcel Dekker, Inc., New York, 1997.
- R.W.Irving and D.F.Manlove. The b-chromatic number of a graph, Discrete Appl. Math., 91 (1999) 127-141.
- G.Jothilakshmi, ” Studies in domination in graphs with special reference to (k, r)-domination and weak convexity”, Madurai kamaraj University Ph.D Thesis, 2009.
- G.Jothilakshmi, A.P.PushpaLatha, S.Suganthi and V.Swaminathan, (k, r)-coloring, International Journal of Mathematics, Computer science and Information Technology., Vol-I December 2008, 211- 219.
- M.Kouider and M.Maheo, some bounds for the b-chromatic number of a graph, Discrete Math., 256(2002), 267-277.
- J.Kratochv’il, Z.Tuza and M.Voigt, On the b-chromatic number of graphs, Proceedings WG02 - 28th International Workshop on Graph-Theoretic Concepts in Computer Science, Cesky Krumlov, Czech Republic, Volume 2573 of Lecture Notes in Computer Science. Springer Verlag 2002.
- E.Sampath Kumar and L.Pushpa Latha, Semi strong chromatic number of a graph, Indian Journal of Pure and Applied Mathematics., 26(1): 35-40, January 1995.
- E.Sampath Kumar and C.V.Venatachalam, Chromatic partitions of a graph, Discrete Math.74 (1989), 227-239.
- H.B.Walikar, B. D. Acharya and E. Sampathkumar, Recent developments in the theory of domination in graphs, MRI Lecture Notes in Math. 1 (1976).
- F.Kramer and H.Kramer,Un probleme de coloration des sommets dun graphe, C.R. Acad. Sci. Paris A 268 (1969) 4648.
- G.Jothilakshmi, A.P.Pushpalatha, G.Sudhalakshmi, S.Suganthi and V.Swaminathan
- Distance r- Coloring and Distance r-Dominator Coloring number of a graph , International Journal of Mathemat- ics Trends and Technology, Volume 5 Number 3, January 2014, Page 242-246.
- G.Jothilakshmi, A.P.Pushpalatha, S.Suganthi and V.Swaminathan,(k, r)-Semi Strong Chromatic Number of a Graph, International Journal of Computer Applications, (09758887),Volume 21 No.2, May 2011.
- G.Jothilakshmi, A.P.Pushpalatha, S.Suganthi and V.Swaminathan,(k, r)-domination and (k, r)- independence number of a graph, International Journal of Computing Technology, Volume 1, No.2, March 2011.
- G.Jothilakshmi, A.P.Pushpalatha, S.Suganthi and V.Swaminathan, Distance r-coloring and distance -r chromatic free, fixed and totally free vertices in a graph, Global journal of Pure and Applied Mathematics, Volume 10, Number 1,2014, pp 53-62.
Year 2016,
Volume: 6 Issue: 2, 315 - 323, 01.12.2016
G. Jothilakshmi
A. P. Pushpalatha
S. Suganthi
V. Swaminathan
References
- R.Balakrishnan, S.Francis Raj and T.Kavaskar, Coloring the Mycielskian, Proceeding of International Conference -ICDM (2008), 53-57.
- G.Chartrand, D.Geller and S.Hedetniemi, A generalization of chromatic number, Proc. Cambridge Philos. Soc. 64 (1968), 265-271.
- M.Chundovsky and P.D.Seymour,The structure of claw-free graphs, manuscript 2004.
- Douglas B.West, Introduction to Graph Theory (Prentice-Hall of India), 2003.
- M.A.Henning, Distance Domination in Graphs:, Advance Topics(Eds:Teresa W. Haynes, Stephen T. Hedetniemi, Peter J. Slater), 321-349, Marcel Dekker, Inc., New York, 1997.
- R.W.Irving and D.F.Manlove. The b-chromatic number of a graph, Discrete Appl. Math., 91 (1999) 127-141.
- G.Jothilakshmi, ” Studies in domination in graphs with special reference to (k, r)-domination and weak convexity”, Madurai kamaraj University Ph.D Thesis, 2009.
- G.Jothilakshmi, A.P.PushpaLatha, S.Suganthi and V.Swaminathan, (k, r)-coloring, International Journal of Mathematics, Computer science and Information Technology., Vol-I December 2008, 211- 219.
- M.Kouider and M.Maheo, some bounds for the b-chromatic number of a graph, Discrete Math., 256(2002), 267-277.
- J.Kratochv’il, Z.Tuza and M.Voigt, On the b-chromatic number of graphs, Proceedings WG02 - 28th International Workshop on Graph-Theoretic Concepts in Computer Science, Cesky Krumlov, Czech Republic, Volume 2573 of Lecture Notes in Computer Science. Springer Verlag 2002.
- E.Sampath Kumar and L.Pushpa Latha, Semi strong chromatic number of a graph, Indian Journal of Pure and Applied Mathematics., 26(1): 35-40, January 1995.
- E.Sampath Kumar and C.V.Venatachalam, Chromatic partitions of a graph, Discrete Math.74 (1989), 227-239.
- H.B.Walikar, B. D. Acharya and E. Sampathkumar, Recent developments in the theory of domination in graphs, MRI Lecture Notes in Math. 1 (1976).
- F.Kramer and H.Kramer,Un probleme de coloration des sommets dun graphe, C.R. Acad. Sci. Paris A 268 (1969) 4648.
- G.Jothilakshmi, A.P.Pushpalatha, G.Sudhalakshmi, S.Suganthi and V.Swaminathan
- Distance r- Coloring and Distance r-Dominator Coloring number of a graph , International Journal of Mathemat- ics Trends and Technology, Volume 5 Number 3, January 2014, Page 242-246.
- G.Jothilakshmi, A.P.Pushpalatha, S.Suganthi and V.Swaminathan,(k, r)-Semi Strong Chromatic Number of a Graph, International Journal of Computer Applications, (09758887),Volume 21 No.2, May 2011.
- G.Jothilakshmi, A.P.Pushpalatha, S.Suganthi and V.Swaminathan,(k, r)-domination and (k, r)- independence number of a graph, International Journal of Computing Technology, Volume 1, No.2, March 2011.
- G.Jothilakshmi, A.P.Pushpalatha, S.Suganthi and V.Swaminathan, Distance r-coloring and distance -r chromatic free, fixed and totally free vertices in a graph, Global journal of Pure and Applied Mathematics, Volume 10, Number 1,2014, pp 53-62.