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- W1877125464 abstract "In this article, 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." @default.
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- W1877125464 date "2015-09-11" @default.
- W1877125464 modified "2023-09-24" @default.
- W1877125464 title "Connectedness and Isomorphism Properties of the Zig-Zag Product of Graphs" @default.
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- W1877125464 doi "https://doi.org/10.1002/jgt.21917" @default.
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