Rainbow Dynamic Coloring in Some Corona Product Graphs

Abstract

Consider a simple, non-trivial, connected graph G, determined by a coloring c : V (G) −→ {1,2,3,....,k} k ∈ N of V(G). In G, a rainbow dynamic coloring is a dynamic coloring where a minimum number of colors is needed such that every two vertices are connected by at least one path whose inner vertices are colored differently. Rainbow dynamic coloring of G, represented as rdyc(G), is the minimum k for which the k-vertex coloring exists. In this work, we compute the rdyc of certain graphs of the corona product. The critical property of the corona product graphs is also discussed.