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Let G be a simple graph with vertex set and edge set 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,doi:10.4236/am.2012.33041 fatcat:cq52xr6largbdj4qdwqnnvkkuy