Coloring of a non-zero component graph associated with a finite dimensional vector space

摘要

A graph is called weakly perfect if its vertex chromatic number equals its clique number. Let V be a vector space over a field F with {alpha 1,..., alpha n} as a basis and theta as the null vector. The non-zero component graph of V with respect to {alpha 1,..., alpha n}, denoted by Gamma(V), is a graph with the vertex set Vtheta and two distinct vertices a and b are adjacent if and only if there exists at least one alpha(i) along which both a and b have non-zero components. In this paper, it is shown that Gamma(V) is a weakly perfect graph. Also, we give an explicit formula for the vertex chromatic number of Gamma(V). Furthermore, it is proved that the edge chromatic number of Gamma(V) is equal to the maximum degree of Gamma(V).