A discourse on the nature of variation of strong chromatic index of line graphs of path graphs, star graphs and cycle graphs and their derivatives

The Strong edge-coloring problem discusses the assignment of colors to the edges of a graph G(V, E) in a manner that distinct colors are assigned to any two edges which are either connected to a common vertex v or a common edge e. The strong chromatic index of a graph G, denoted by [Formula: see text], refers to the least number of colors necessary to define such a coloring for G. In our article, we present results on [Formula: see text] pertaining to line graphs generated from graphs which are constructed from paths, star graphs and cycles.