Generalized X-join of graphs and their automorphisms

Abstract

In this paper, we first introduce a new product of finite graphs as a generalization of the X-join of graphs. We then give necessary and sufficient conditions for a graph to be isomorphic to a generalized X-join. As a main result, we give necessary and sufficient conditions under which the full automorphism group of a generalized X-join is equal to the generalized wreath product of the automorphism groups of its factors. © 2024 Society of Mathematicians, Physicists and Astronomers of Slovenia. All rights reserved.