ON THE INJECTIVE CHROMATIC NUMBER OF SPLITTING GRAPH AND SHADOW GRAPH OF CERTAIN REGULAR AND BIREGULAR GRAPHS

ON THE INJECTIVE CHROMATIC NUMBER OF SPLITTING GRAPH AND SHADOW GRAPH OF CERTAIN REGULAR AND BIREGULAR GRAPHS

C. K. Bhanupriya , M. S. Sunitha

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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.

Keywords

Injective coloring; injective chromatic number; splitting graph; shadow graph.