Acyclic Coloring of Certain Graphs

Abstract

A graph G with acyclic coloring has no two adjacent vertices with the same color and no bichromatic cycle. Also, the coloring results in a forest when any two-color classes are combined. The concept of acyclic coloring plays a pivotal role in the computation of Hessians, Kekule structures classification, coding theory, and statistical mechanics. In this paper, the acyclic chromatic number of generalized fan graph, generalized Möbius ladder graph and flower snark graph have been determined.