Injective Chromatic Sum and Injective Chromatic Polynomials of Graphs

The injective chromatic number x+ i(G) [5] of a graph 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. In this paper we de ne injec- tive chromatic sum and injective strength of a graph and obtain the injective chromatic sum of complete graph, paths, cycles, wheel graph and complete bi- partite graph. We also suggest bounds for injective chromatic sum. The in- jective chromatic sum of graph complements, join, union, product and corona is discussed.The concept of injective chromatic polynomial is introduced and computed for complete graphs, bipartite graphs, cycles etc. The bounds for the injective chromatic polynomial of trees is suggested.