\(b\)-Chromatic number of some wheel related graphs

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DOI:

https://doi.org/10.26637/mjm204/015

Abstract

A proper coloring \(f\) is a \(b\)-coloring of the vertices of graph \(G\) such that in each color class there exists a vertex that has neighbours in every other color classes. The \(b\)-chromatic number \(\varphi(G)\) of a graph \(G\) is the largest integer \(k\) for which \(G\) admits a \(b\)-coloring with \(k\) colors. If \(\chi(G)\) is the chromatic number of \(G\) and \(b\)-coloring exists for every integer \(k\) satisfying the inequality \(\chi(G) \leq k \leq \varphi(G)\) then \(G\) is called \(b\)-continuous. The \(b\)-spectrum \(S_b(G)\) of a graph \(G\) is the set of \(k\) integers(colors) for which \(G\) has a \(b\)-coloring. We investigate \(b\)-chromatic number for the graphs obtained from wheel \(W_n\) by means of duplication of vertices. We also discuss \(b\)-continuity and \(b\)-spectrum for such graphs.

Keywords:

\(b\)-Coloring, \(b\)-Continuity , \(b\)-Spectrum

Mathematics Subject Classification:

05C15, 05C76
  • Pages: 482-488
  • Date Published: 01-10-2014
  • Vol. 2 No. 04 (2014): Malaya Journal of Matematik (MJM)

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Published

01-10-2014

How to Cite

S. K. Vaidya, and M. S. Shukla. “\(b\)-Chromatic Number of Some Wheel Related Graphs”. Malaya Journal of Matematik, vol. 2, no. 04, Oct. 2014, pp. 482-8, doi:10.26637/mjm204/015.