Spectral analysis of the wreath product of a complete graph with a cocktail party graph

Francesco Belardo, Matteo Cavaleri, Alfredo Donno

Abstract


Graph products and the corresponding spectra are often studied in the literature. A special attention has been given to the wreath product of two graphs, which is derived from the homonymous product of groups. Despite a general formula for the spectrum is also known, such a formula is far from giving an explicit spectrum of the compound graph. Here, we consider the latter product of a complete graph with a cocktail party graph, and by making use of the theory of circulant matrices we give a direct way to compute the (adjacency) eigenvalues.

Keywords


Wreath Product of Graphs; Complete Graph; Cocktail Party Graph; Adjacency Matrix; Spectrum

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DOI: http://dx.doi.org/10.1478/AAPP.96S2A1

Copyright (c) 2018 Francesco Belardo, Matteo Cavaleri, Alfredo Donno

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