Some Results on Edge Cover Coloring of Double Graphs

Jihui Wang, Qiaoling Ma

School of Mathematical Sciences, University of Jinan, Jinan, China.

DOI: 10.4236/am.2012.33041                

Abstract

Let G be a simple graph with vertex set V(G) and edge set E(G). An edge coloring C of G is called an edge cover coloring, if each color appears at least once at each vertex . The maximum positive integer k such that G has a k edge cover coloring is called the edge cover chromatic number of G and is denoted by . It is known that for any graph G, . If , then G is called a graph of CI class, otherwise G is called a graph of CII class. It is easy to prove that the problem of deciding whether a given graph is of CI class or CII class is NP-complete. In this paper, we consider the classification on double graph of some graphs and a polynomial time algorithm can be obtained for actually finding such a classification by our proof.

Keywords

Edge Cover Coloring; Classification; Double Graph

Conflicts of Interest

The authors declare no conflicts of interest.

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