\(b\)-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 \(C(K_{1,n,n,n})\), \(M(K_{1,n,n,n})\), \(T(K_{1,n,n,n})\) and \(L(K_{1,n,n,n})\), respectively.

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References

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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 Articles

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