b-Chromatic Sum of Mycielskian of Paths

A b-coloring of a graph G is a proper coloring of the vertices of G such that there exist a vertex in each color class joined to at least one vertex in each other color classes. The b-chromatic number of a graph G, denoted by ϕ(G), is the largest integer k such that G has a b-coloring with k colors. The b-chromatic sum of a graph G(V, E), denoted by ϕ′(G) is defined as the minimum of sum of colors c(v) of v for all v∈V in a b-coloring of G using ϕ(G) colors, where the colors are taken as the positive integer. In this paper, the b-chromatic sum of Mycielskian of a path is discussed.