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 \r, 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 ᵣ (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 i^th copy of H to the i^th 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.