On r-Hued Coloring of Corona Product of Some Graphs

An r-hued coloring of a graph G is a proper k-coloring of graph G such that the neighbours of any vertex u accept at least min , d(u)\ different colors. The r-hued chromatic number is the minimum k such that graph G has an r-hued k-coloring, it is denoted by χᵣ(G). The corona product G∘ H of two graphs G and H is obtained by taking one copy of G and |V(G)| copies of H and joining every vertex of iᵗʰ copy of H to the iᵗʰ copy of G, where 1≤ i≤ |V(G)|. In this paper, we obtain the r-hued chromatic number of corona product of two graphs G and H, denoted by G∘ H. First, we consider G∘ H, where G is the path graph and H is any simple graph like complete graph. Secondly, we consider G as the complete graph and H as the path graph. Finally we consider G as the cycle graph and H as the path graph.