Edge incident 2-edge coloring sum of graphs

Abstract

The edge incident 2-edge coloring number, ψ′ein2(G), of a graph G is the highest coloring number used in an edge coloring of a graph G such that the edges incident to an edge e = uv in G is colored with at most two distinct colors. The edge incident 2-edge coloring sum of a graph G, denoted as Pein2′ (G), is the greatest sum among all the edge incident 2-edge coloring of graph G which receives maximum ψ′ein2(G) colors. The main objective of this paper is to study the edge incident 2-edge coloring sum of graphs and find the exact values of this parameter for some known graphs.