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SOME RESULTS ON THE DISTANCE r-b-COLORING IN GRAPHS

Year 2016, Volume: 6 Issue: 2, 315 - 323, 01.12.2016

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

Abstract

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.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

G. Jothilakshmi This is me

A. P. Pushpalatha This is me

S. Suganthi This is me

V. Swaminathan This is me

Publication Date December 1, 2016
Published in Issue Year 2016 Volume: 6 Issue: 2

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