New families of equitable graphs

Abstract

A labeling f of the vertices of a graph G is said k-equitable if each weight induced by f on the edges of G, appears exactly k times. A graph G is said equitable if for every proper divisor k of its size, the graph G has a k-equitable labeling. Only two families of equitable graphs are known until now, the cycles and the linear forest. In this paper we present some families of equitable graphs related with the already known.