On the injective chromatic number of splitting graph and shadow graph of certain regular and biregular graphs

Abstract

The injective chromatic number of a graph G, denoted by χi(G) is the minimum number of colors needed to color the vertices of G such that two vertices with a common neighbor are assigned distinct colors. The splitting graph and shadow graph are larger graphs obtained from a graph by a construction. In this article, χi(G) of splitting graph and shadow graph of certain classes of graphs are obtained in terms of number of vertices. Also obtained a lower and upper bound for the injective chromatic number of splitting graph and shadow graph of any graph.