On b-coloring of central graph of some graphs

Year 2019, Volume: 68 Issue: 1, 1229 - 1239, 01.02.2019

M. Kalpana D. Vijayalakshmi

https://doi.org/10.31801/cfsuasmas.516089

Cited By: 2

Abstract

The b-chromatic number of G, denoted by ϕ(G), is the maximum k for which G has a b-coloring by k colors. A b-coloring of G by k colors is a proper k-coloring of the vertices of G such that in each color class i there exists a vertex x_{i} having neighbors in all the other k-1 color classes. Such a vertex x_{i} is called a b-dominating vertex, and the set of vertices {x₁,x₂…x_{k}} is called a b-dominating system. In this paper, we are going to investigate on the b-chromatic number of Central graph of Triangular Snake graph, Sunlet graph, Helm Graph, Double Triangular Snake graph, Gear graph, and Closed Helm graph are denoted as C(T_{n}), C(S_{n}), C(H_{n}), C(DT_{n}), C(G_{n}), C(CH_{n}) respectively.

Keywords

b-coloring , b-chromatic number , central graph

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