On δ(k)-coloring of generalized Petersen graphs

Abstract

The chromatic number, [Formula: see text] of a graph [Formula: see text] is the minimum number of colors used in a proper coloring of [Formula: see text]. In an improper coloring, an edge [Formula: see text] is bad if the colors assigned to the end vertices of the edge is the same. Now, if the available colors are less than that of the chromatic number of graph [Formula: see text], then coloring the graph with the available colors leads to bad edges in [Formula: see text]. In this paper, we use the concept of [Formula: see text]-coloring and determine the number of bad edges in generalized Petersen graph ([Formula: see text]). The number of bad edges which result from a [Formula: see text]-coloring of [Formula: see text] is denoted by [Formula: see text].