On resistance of graphs

An edge-coloring of a graph GG with integers is called an interval coloring if all colors are used, and the colors of edges incident to any vertex of GG 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.