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

Yıl 2016, Cilt: 6 Sayı: 2, 315 - 323, 01.12.2016

Öz

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.

Kaynakça

  • 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.
Yıl 2016, Cilt: 6 Sayı: 2, 315 - 323, 01.12.2016

Öz

Kaynakça

  • 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.
Toplam 19 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

G. Jothilakshmi Bu kişi benim

A. P. Pushpalatha Bu kişi benim

S. Suganthi Bu kişi benim

V. Swaminathan Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2016
Yayımlandığı Sayı Yıl 2016 Cilt: 6 Sayı: 2

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