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Some Results on Edge Cover Coloring of Double Graphs

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DOI: 10.4236/am.2012.33041    3,402 Downloads   5,709 Views   Citations

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.

Conflicts of Interest

The authors declare no conflicts of interest.

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.

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