Total Coloring for Several Families of 4-Regular Circulant Graphs

Abstract

4-Regular circulant graphs are among the most important classes of graphs, and their total coloring has attracted much attention in recent years. Nevertheless, determining the total chromatic numbers for most 4-regular circulant graphs remains an open problem, despite considerable efforts. In this paper, we address this issue and determine the total chromatic numbers for several families of 4-regular circulant graphs.