(untitled) (Journal of Informatics and Mathematical Sciences, 2017)
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. The \(b\)-chromatic number of a graph \(G\), denoted by \(b(G)\), is the maximal integer \(k\) such that \(G\) may have a \(b\)-coloring by \(k\) colors. In this paper, we investigate the \(b\)-chromatic number of Central graph, Middle graph, Total graph and Line graph of Triple Star graph, denoted by \(C(K_1,n,n,n)\), \(M(K_1,n,n,n)\), \(T(K_1,n,n,n)\) and \(L(K_1,n,n,n)\), respectively.