Spectrum, distance spectrum, and Wiener index of wreath products of complete graphs

Alfredo Donno


We describe the adjacency matrix and the distance matrix of the wreath product of two complete graphs, and we give an explicit computation of their spectra. As an application, we deduce the spectrum of the transition matrix of the Lamplighter random walk over a complete base graph, with a complete color graph. Finally, an explicit computation of the Wiener index is given.


Wreath product of complete graphs, adjacency matrix, distance matrix, spectrum, distance spectrum, Wiener index

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DOI: https://doi.org/10.26493/1855-3974.1117.7ba

ISSN: 1855-3974

Issues from Vol 6, No 1 onward are partially supported by the Slovenian Research Agency from the Call for co-financing of scientific periodical publications