B-chromatic number of extended corona of some graphs

S Kiruthika ,N Mohanapriya

doi:10.26524/krj.2020.30

Abstract

In this paper we find out the b-chromatic number for the extended corona of path with complete on the same order Pn.kn path on order n with star graph on order n+1 say ,Pn.kn+1 cycle with complete on the same order ,Cn.kn cycle on order n with star graph on order n+1 say Cn.kn+1, star graph on order n+1 with complete on order n say kn+1.Kn ,complete on order n with star graph on b-coloring, b-chromatic number, extended corona. order n+1 say kn.Kn+1 respectively.

Highlights

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
This parameter has been derived by Irving and Manlove [3] in the year 1999 and gave an introduction about the concept of b-coloring and showed that the problem of determining φ(G) is NP-hard for general graphs but it is polynomialtime solvable for trees.Since every b-coloring is a proper coloring, we obtain that the chromatic number (G) is a lower bound for φ(G)
If we introduce any new color to any vertex in the graph, that will not adjacent to all other color class, b-coloring with colors is not possible