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

AbstractA set is called a general position set of a graph G if any triple set V0 of R is non-geodesic, that is, three elements of V0 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(G2) and gp(G). We deduce a formula of and provide the upper bound on gp(G2)−gp(G) for general block graphs G. Moreover, we determine the gp-number for the square of trees.Mathematics Subject Classification (2020): 05C1205C0505C76Key words: General position setgeneral position numberpower graphs