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Constructing families of cospectral regular graphs

Published online by Cambridge University Press:  30 June 2020

M. Haythorpe
Affiliation:
Flinders University, 1284 South Road, Tonsley, SA 5042, Australia
A. Newcombe*
Affiliation:
Flinders University, 1284 South Road, Tonsley, SA 5042, Australia
*
*Corresponding author. Emails: [email protected], [email protected]

Abstract

A set of graphs are called cospectral if their adjacency matrices have the same characteristic polynomial. In this paper we introduce a simple method for constructing infinite families of cospectral regular graphs. The construction is valid for special cases of a property introduced by Schwenk. For the case of cubic (3-regular) graphs, computational results are given which show that the construction generates a large proportion of the cubic graphs, which are cospectral with another cubic graph.

Type
Paper
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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Footnotes

Research partially supported by ARC Discovery Grant DP150100618.

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