On the general position number of the k-th power graphs

Abstract

A set is called a general position set of a graph G if any triple set V 0 of R is non-geodesic, that is, three elements of V 0 cannot lie on the same geodesic of G. The general position number gp(G) of a graph G is the cardinality of a largest general position set of G. The k-th power, Gk , of a graph G is obtained from G by adding a new edge between each pair of vertices with a distance of at most k in G. In this paper we establish the bounds for gp(Gk ) and and give an explicit formula of . Also we consider the relation between gp(G 2) and gp(G). We deduce a formula of and provide the upper bound on gp(G 2)−gp(G) for general block graphs G. Moreover, we determine the gp-number for the square of trees.