Interval edge coloring of some classes operations graph of paths

Abstract With the wide application of combinatorial optimization problems in optics, we were inspired by optics and studied the interval edge coloring problem of operational graphs. The maximum value of t for an interval t -coloring is denoted by W(G) , which is a proper edge-coloring of a graph G using colors 1, 2, …, t . In this coloring process, all colors are used, and the color of the edges associated with each vertex has a different color, forming an interval of integers. In this paper, we prove that G is interval colorable and we give a lower bound on W(G) if and only if G is a generalized Mycielski graph, double graph or middle graph of the path.