Coloring index of the line graph and the complete two-sided graph Enlightenment and extensions

Abstract

The color index of graph G is the minimum number of colors required for coloring edges so that, no two edges with a common vertex are coloring in the same color, [3].

The line graph of a graph G is a graph whose vertices are the G edges, and between two vertices in the line graph, there is an edge if they represent two edges in G, which have a common vertex, [1].

Here in this paper we will refine and expand the connections between the color index and the line graph.