Star Chromatic Number of the Edge Corona of Two Graph

Abstract

Graph products are introduced to obtain information on large graphs from similar information on smaller graphs. One of the most prominent graph products is Corona product of graphs. A more applicable version of it called as the edge corona was introduced ten years ago. A star coloring of an undirected graph G is an allocation of colors to every element of vertex set of the graph G such that no path of order four in G isbicolored. The star chromatic number of G is the minimum colors required to star color the graph G. Nowadays, the concept of star coloring is very much useful in tracebacking the IP addresses in networks. In this paper, we establish the exact value of the star chromatic number of edge corona product of path graph with complete graph, cycle graph, star graph, complete bipartite graph and any simple graph. Also, we have found the same for edge corona product of star graph with path graph, cycle graph, complete and any simple graph.