Strong Edge Coloring of Some Classes of Unicyclic Graphs

Abstract

Let \textit{G } be an undirected simple graph. A strong edge coloring of a graph \textit{G } is a function $f : E \to \{1, 2,\dots, k\}$ such that $f(e_{1} )\ne f(e_{2} )$ whenever $e_{1} $ and $e_{2} $ lie within distance 2 from each other. In other words, no two edges lie on a path of length 3 receive same colors. The smallest number of colors essential for strong edge coloring of a graph \textit{G } is entitled as strong chromatic index and is represented by $\chi '_{s} (G)$. In this paper, we investigate strong chromatic index of some classes of unicyclic graphs.