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Properties of the Generalized Zig-Zag Product of Graphs

Samuel Cooper·Dominic Dotterrer·Stratos Prassidis
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Abstract

The operation of zig-zag products of graphs is the analogue of the semidirect product of groups. Using this observation, we present a categorical description of zig-zag products in order to generalize the construction for the category of simple graphs. Also, we examine the covering properties of zig-zag products and we utilize these results to estimate their spectral invariants in general. In addition, we provide specific spectral analysis for some such products.

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Samuel Cooper, Dominic Dotterrer, Stratos Prassidis. 2006-07-14. Properties of the Generalized Zig-Zag Product of Graphs. https://arxiv.org/abs/math/0607352

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