The Chromatic Index of a Graph G Depending on the Subgraph Induced by the Vertices of Maximum Degree

Abstract

The $\mathrm{\Delta }$-subgraph $G_{\mathrm{\Delta }}$ of a simple graph $G$ is the subgraph induced by the vertices of maximum degree of $G$. In this paper, we obtain some results about the construction of a graph $G$ if the graph $G$ is Class 2 and the structure of $G_{\mathrm{\Delta }}$ is particularly simple.