On δ(k)-coloring of generalized Petersen graphs

The chromatic number, chi(G) of a graph G is the minimum number of colors used in a proper coloring of G. In an improper coloring, an edge uv 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 G, then coloring the graph with the available colors leads to bad edges in G. In this paper, we use the concept of delta((k))-coloring and determine the number of bad edges in generalized Petersen graph (P(n,t)). The number of bad edges which result from a delta((k))-coloring of G is denoted by b(k)(G).