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Constructing families of cospectral regular graphs

Part of: Graph theory

Published online by Cambridge University Press:  30 June 2020

M. Haythorpe  and
A. Newcombe
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: michael.haythorpe@flinders.edu.au, alex.newcombe@flinders.edu.au
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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.

MSC classification

Primary: 05C50: Graphs and linear algebra (matrices, eigenvalues, etc.)
Secondary: 05C07: Vertex degrees
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 29 , Issue 5 , September 2020 , pp. 664 - 671
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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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