On Mf-Edge Colorings of Graphs

Abstract

Abstract An edge coloring φ of a graph G is called an Mf-edge coloring if | φ(v)| ≤ f(v) for every vertex v of G, where φ(v) is the set of colors of edges incident with v and f is a function which assigns a positive integer f(v) to each vertex v. Let 𝒦f (G) denote the maximum number of colors used in an Mf-edge coloring of G. In this paper we establish some bounds on 𝒦f(G), present some graphs achieving the bounds and determine exact values of 𝒦f(G) for some special classes of graphs.