Some Results on Edge Cover Coloring of Double Graphs

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.

Let

Cite this paper

J. Wang and Q. Ma, "Some Results on Edge Cover Coloring of Double Graphs,"*Applied Mathematics*, Vol. 3 No. 3, 2012, pp. 264-266. doi: 10.4236/am.2012.33041.

J. Wang and Q. Ma, "Some Results on Edge Cover Coloring of Double Graphs,"

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