H-extension of graphs

Abstract

We consider the problem of constructing a graph G* from a collection of isomorphic copies of a graph G in such a way that for every two copies of G, either no vertices or a section graph isomorphic to a graph H is identified. It is shown that if G can be partitioned into vertex-disjoint copies of H, then G* can be made to have at most |H| orbits. A condition on G so that G* can be vertextransitive is also included. © 1984 Akadémiai Kiadó.