On Injective Coloring of Graphs and Chromaticity of Fuzzy Graphs

The concepts of injective chromatic sum and injective strength of a graph based on injective coloring of vertices are introduced and the injective chromatic sum of complete graph, paths, cycles, wheel graph and complete bipartite graph are obtained. The injective 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, wheel graphs and trees. The nature of the coefficients of injective chromatic polynomials of complete graphs, wheel graphs and cycles are studied. Injective chromatic polynomials on operations such as union, join, Cartesian product and corona of graphs are obtained.Coloring in a fuzzy graph is studied and coloring based on strong arcs is introduced.