Star-Rainbow Dynamic Coloring in Some Corona Product Graphs

Abstract

Let G be a connected graph which is nontrivial, defined a coloring c: V(G)\( \to\) {1, 2, …., k}, k N of the vertices of G. A rainbow dynamic coloring of a graph is a dynamic coloring and minimum number of colors required, such that every pair of vertices is connected by at least one path whose within vertices have different colors. Further, G is said to be star-rainbow dynamic colored if every path on four vertices in it is rainbow dynamic colored. The minimum k for which there exist a k-vertex coloring called the star rainbow dynamic coloring of G, denoted by strrdyc(G). In this paper we determine some corona product graphs involving Petersen graph, path and complete graph, path and star graph and star and complete graph and find strrdyc(G) for such graphs.