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.
Spectral analysis of the wreath product of a complete graph with a cocktail party graph / Belardo, Francesco; Cavaleri, Matteo; Donno, Alfredo. - In: ATTI DELLA ACCADEMIA PELORITANA DEI PERICOLANTI, CLASSE DI SCIENZE FISICHE, MATEMATICHE E NATURALI. - ISSN 1825-1242. - 96:S2(2018), pp. 1-11. [10.1478/AAPP.96S2A1]
Spectral analysis of the wreath product of a complete graph with a cocktail party graph
Francesco Belardo;
2018
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.| File | Dimensione | Formato | |
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