On Proper Coloring And Acyclic Coloring Of Some Graphs

Abstract

In the following century, a vast amount of work and theories were developed to reduce the number of colors to four, until the four color theorem was finally proved in 1976 by Kenneth Appel and Wolfgang Haken, Perhaps surprisingly, the proof went back to the ideas of Heawood and Kemne and largely discarded the intervening developments. The proof the four color theorem is also noteworthy for being the first major computer-aided proof. When used without any qualification a coloring of a graph is almost always a proper vertex coloring of the graphs, vertices with colors such that no two vertices sharing the same edge have the same color. Partial K-coloring, Star coloring, Acyclic coloring, Grundy coloring, Quorum coloring, Hamiltonian partition coloring, Harmonious coloring, Rainbow coloring, b-coloring etc., are different types of coloring. In this dissertation, we present the proper coloring and Acyclic coloring of H-graphs, Jelly fish graph, Umbrella graph circular ladder graph, Triangular belt graph, snake graphs, and some corona graphs.