A switching method for constructing cospectral gain graphs

Aida Abiad Monge; Francesco Belardo; Antonina Khramova

doi:10.1016/j.disc.2023.113838

A switching method for constructing cospectral gain graphs

Aida Abiad Monge (Corresponding author)
, Francesco Belardo
, Antonina Khramova

Algebraic Combinatorics

Research output: Contribution to journal › Article › Academic › peer-review

4 Citations (Scopus)

95 Downloads (Pure)

Abstract

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.

Original language	English
Article number	113838
Number of pages	9
Journal	Discrete Mathematics
Volume	347
Issue number	4
DOIs	https://doi.org/10.1016/j.disc.2023.113838
Publication status	Published - Apr 2024

Funding

We would like to thank the referees for their insightful and helpful comments. Aida Abiad is partially supported by FWO ( Research Foundation Flanders ) via the grant 1285921N . This research is supported by NWO ( Dutch Research Council ) via an ENW-KLEIN-1 project ( OCENW.KLEIN.475 ).

Funders	Funder number
Fonds Wetenschappelijk Onderzoek	1285921N
Nederlandse Organisatie voor Wetenschappelijk Onderzoek	OCENW.KLEIN.475

Keywords

Adjacency matrix
Cospectral
Gain graph
Switching

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10.1016/j.disc.2023.113838

pdfFinal published version, 313 KBLicence: CC BY

http://arxiv.org/abs/2304.03555

Cite this

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AB - 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.

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KW - Gain graph

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A switching method for constructing cospectral gain graphs

Abstract

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Keywords

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