Another look at geodetic and hull numbers of a graph

Abstract

Given a connected graph G and two vertices u and v in G, I_G[u,v] is the set consisting of u, v and all vertices lying on some u−v geodesic of G. A subset S of V(G) is called a geodetic set of G if I_G[S] = V(G), where I_G[S]=∪_u,v ∈ S I_G[u,v]. The geodetic number of G, denoted by g(G) is the smallest cardinality of a geodetic set of G. In this paper, we give the geodetic number of the composition of a complete graph K_n and a (connected) graph G.