Irregular Coloring in Interconnection Networks

Abstract

Coloring is one of the most important aspects of graph theory. Specially, graphs embedded on surfaces undergo three types of colorings: vertex colorings, edge colorings, and region colorings. When it comes to graph colorings, the vertex colorings have received the most attention and are the most widely used. A coloring of a graph is an assignment of colors to its vertices so that no two adjacent vertices have the same color. A color class is the independent set of all vertices with a single color..... newline