A Note On Unary Operatıons On Graphs And Theır Acyclıc Colorıng

Abstract

An acyclic coloring is a proper vertex coloring in which no cycle in the graph is bichromatic or the subgraph induced by any two colors is acyclic. The acyclic chromatic number a(G) of a graph G is the least number of colors in an acyclic coloring of G. In this paper, acyclic coloring of middle and central graph of some graphs are investigated. For any graph G, a relation between the acyclic chromatic number and acyclic chromatic index of its line graph is derived, and using this relation, acyclic chromatic index of line graph of n -dimensional graphs like hypercube, mesh and torus are analyzed.