Connectedness and isomorphism properties of the zig-zag product of graphs

Research output: Contribution to journalArticle

Abstract

In this paper we investigate the connectedness and the isomorphism problems for zig-zag products of two graphs. A sufficient condition for the zig-zag product of two graphs to be connected is provided, reducing to the study of the connectedness property of a new graph which depends only on the second factor of the graph product. We show that, when the second factor is a cycle graph, the study of the isomorphism problem for the zig-zag product is equivalent to the study of the same problem for the associated pseudo-replacement graph. The latter is defined in a natural way, by a construction generalizing the classical replacement product, and its degree is smaller than the degree of the zig-zag product graph.
Two particular classes of products are studied in detail: the zig-zag product of a complete graph with a cycle graph, and the zig-zag product of a 4-regular graph with the cycle graph of length 4. Furthermore, an example coming from the theory of Schreier graphs associated with the action of self-similar groups is also considered: the graph products are completely determined and their spectral analysis is developed.
Original languageEnglish
Pages (from-to)120
Number of pages151
JournalJournal of graph theory
Volume83
Issue number2
DOIs
Publication statusPublished - 2016

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Theoretical

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