Properties of the Generalized Zig-Zag Product of Graphs

2006/07/14 by Samuel Cooper, Cooper, Samuel, Dominic Dotterrer +3
Mathematics · #05C50 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C50

paper · pdf · doi:10.48550/arxiv.math/0607352

15 pages

arxiv created 2006/07/14 · arxiv updated 2009/12/01

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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