On normal Cayley graphs and hom-idempotent graphs
type: Item
instance of: scholarly article
title: On normal Cayley graphs and hom-idempotent graphs
zbMATH Open document ID: 0916.05032
author: Benoît Larose
author: François Laviolette
author: Claude Tardif
published in: European Journal of Combinatorics
publication date: 1999-07-07T00:00:00Z
review text: This paper studies the cartesian product of graphs as an operation on classes of homomorphically equivalent graphs. The theory of graph homomorphisms is more in the spirit of coloring theory than of isomophism questions, but for some graphs (called cores) the only homomorphisms are automorphisms, and the authors use the automorphism group of a core graph to create a Cayley graph from an arbitrary graph. One of the main results of this paper is that a graph is ``hom-idempotent'' (homomorphically equivalent to its cartesian product with itself) if and only if it is homomorphically equivalent to a normal Cayley graph (``normal'' meaning that the edges are defined by a normal subset of the group). The authors also characterize ``weakly hom-idempotent'' graphs (a generalization of hom-idempotent) and include some related results and examples.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C75
Mathematics Subject Classification ID: 05C15
zbMATH DE Number: 1235014
zbMATH Keywords: graph homomorphism
zbMATH Keywords: cartesian product
zbMATH Keywords: weakly hom-idempotent
reviewed by: Albert J. Goodman
MaRDI profile type: Publication
full work available at URL: eujc.1998.0234
OpenAlex ID: W2068223765
DOI: 10.1006/EUJC.1998.0234
description: scientific article; zbMATH DE number 1235014