A switching method for constructing cospectral gain graphs

A gain graph over a group G, also referred to as G-gain graph, is a graph where an element of a group G, called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. Gain graphs can be regarded as a generalization of signed graph...

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Bibliographic Details
Published in:Discrete mathematics 2024-04, Vol.347 (4), p.113838, Article 113838
Main Authors: Abiad, Aida, Belardo, Francesco, Khramova, Antonina P.
Format: Article
Language:English
Subjects:
Adjacency matrix
Cospectral
Gain graph
Switching
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Summary:A gain graph over a group G, also referred to as G-gain graph, is a graph where an element of a group G, called gain, is assigned to each oriented edge, in such a way that the inverse element is associated with the opposite orientation. Gain graphs can be regarded as a generalization of signed graphs, among others. In this work, we show a new switching method to construct cospectral gain graphs. Some previous methods known for graph cospectrality follow as a corollary of our results.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2023.113838