On b-coloring of central graph of some graphs

Authors : M KALPANA, D VİJAYALAKSHMİ

Pages : 1229-1239

Doi:10.31801/cfsuasmas.516089

View : 20 | Download : 16

Publication Date : 2019-02-01

Article Type : Research Paper

Abstract :The b-chromatic number of G, denoted by ϕinsert ignore into journalissuearticles values(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 Cinsert ignore into journalissuearticles values(T_{n});, Cinsert ignore into journalissuearticles values(S_{n});, Cinsert ignore into journalissuearticles values(H_{n});, Cinsert ignore into journalissuearticles values(DT_{n});, Cinsert ignore into journalissuearticles values(G_{n});, Cinsert ignore into journalissuearticles values(CH_{n}); respectively.
Keywords : b coloring, b chromatic number, central graph