The METRIC COLORING OF RELATED WHEEL GRAPHS

Abstract

In this paper, graphs are finite and connected graph. Let  be a vertex coloring of a graph G where two adjacent vertices may be colored the same color. Consider the color classes . For a vertex , representation color of v is the k-vector , where . If  for every two adjacent vertices u and v of G, then f is called a metric coloring of G. The minimum k for which G has a metric k-coloring is called the metric chromatic number of G and is denoted by . In this paper, we study the metric chromatic numbers of related wheel graphs namely double wheel graph, web graph, friendship graph and helm graph.