On Resistance of Graphs.
Petros A. Petrosyan, Hovhannes Sargsyan · Cologne Twente Workshop on Graphs and Combinatorial Optimization · 2009
Abstract An edge-coloring of a graph G with integers is called an interval coloring if all colors are used, and the colors of edges incident to any vertex of G are distinct and form an interval of integers. It is known that not all graphs have interval colorings, and therefore it is expedient to consider a measure of closeness for a graph to be interval colorable. In this paper we introduce such a measure (resistance of a graph) and we determine the exact value of the resistance for some classes of graphs.