b-coloring of Central Graph of Triangular Snake

Abstract

A given k-coloring c of a graph $G=(V,E)$ is a b-coloring if for every color class $c_i$, $1 \leq i \leq k$, there is a vertex colored i whose neighborhood intersect every other color class $c_j$, $1 \leq i \leq k$, of c. The b-chromatic number of G is the greatest integer k such that G admits a b-coloring with k colors. In this paper, the authors find the b-chromatic number of central graph of the triangular snake.