b-Chromatic Number of Triple Star Graph Families

Authors

  • D. Vijayalakshmi Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029
  • M. Kalpana Department of Mathematics, Kongunadu Arts and Science College, Coimbatore 641029

DOI:

https://doi.org/10.26713/jims.v9i3.1014

Keywords:

Central graph, Middle graph, Total graph, Line graph, Star graph, b-coloring, bchromatic number

Abstract

A $b$-coloring of a graph G is a proper coloring of the vertices of G such that there exists a vertex in each color class joined to atleast a vertex in each other color class, such a vertex is called a dominating vertex. The b-chromatic number of a graph G, denoted by b(G), is the maximal integer k such that G may have a b-coloring by k colors. In this paper, we investigate the b-chromatic number of Central graph, Middle graph, Total graph and Line graph of Triple Star graph, denoted by C(K1,n,n,n), M(K1,n,n,n), T(K1,n,n,n) and L(K1,n,n,n), respectively.

Downloads

References

J.A. Bondy and U.S.R. Murty, Graph Theory with Applications, MacMillan, London (1976).

B. Effantin, The b-chromatic number of power graphs of complete caterpillars, J. Discrete Math. Sci. Cryptogr. 8 (2005), 483 – 502.

B. Effantin and H. Kheddouci, The b-chromatic number of some power graphs, Discrete Math. Theor. Comput. Sci. 6 (2003), 45 – 54.

B. Effantin and H. Kheddouci, Exact values for the b-chromatic number of a power complete k-ary tree, J. Discrete Math. Sci. Cryptogr. 8 (2005), 117 – 129.

R.W. Irving and D.F. Manlove, The b-chromatic number of a graph, Discrete Appl. Math. 91 (1999), 127 – 141.

M. Kouider and A. El Sahili, About b-colouring of regular graphs, Rapport de Recherche No. 1432, CNRS-Universit´e Paris Sud LRI, 02/(2006).

S. Kla˘vzar and M. Jakovac, The b-chromatic number of cubic graphs, Preprint series 47 (January 27 2009), 1067.

V.J. Vernold, M. Venkatachalam and M.M. Akbar Ali, A note on achromatic coloring of star graph families, Filomat 23(3) (2009), 251 – 255.

V.J. Vernold and M. Venkatachalam, The b-chromatic number of star graph families, Le Mathematice (2010), 119 – 125.

Downloads

Published

2017-10-30
CITATION

How to Cite

Vijayalakshmi, D., & Kalpana, M. (2017). b-Chromatic Number of Triple Star Graph Families. Journal of Informatics and Mathematical Sciences, 9(3), 937–947. https://doi.org/10.26713/jims.v9i3.1014

Issue

Vol. 9 No. 3 (2017)

Section

Research Article

License

Authors who publish with this journal agree to the following terms:
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.