Abstract:

Let G be a finite undirected simple graph with chromatic index \chi ' (G). For a minimal proper edge coloring \psi: E(G) \to \{1,2,..., \chi ' (G)\} in G, an edge covering set S is an edge covering coloring set if each color class in \{1,2,...,\chi ' (G)\} appears in some edge in S. The edge cover coloring number of G, denoted by \chi_{\alpha} ' (G), is the minimum cardinality taken over all possible edge cover coloring sets and all minimal proper edge colorings in G. This paper discusses the problem of finding the edge cover coloring number in graphs, particularly for paths, cycles, complete graphs, wheels, and (n,k)-tadpole graphs.