Non-existence of co-spectral simple connected graphs with small number of edges

We prove that if the number of edges does not exceed 7 then the asymptotics of eigenvalues of the Dirichlet problem uniquely determine the shape of the graph.

Publication Details

Journal
ArXiv.org
Published
2025-08-27
Primary Topic
Geochemistry and Geologic Mapping
Type
article
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article

Non-existence of co-spectral simple connected graphs with small number of edges

ArXiv.org
Geochemistry and Geologic Mapping
article

Non-existence of co-spectral simple connected graphs with small number of edges

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Abstract

We prove that if the number of edges does not exceed 7 then the asymptotics of eigenvalues of the Dirichlet problem uniquely determine the shape of the graph.

ArXiv.org
Openalex Percentile: Top 60%
Geochemistry and Geologic Mapping
Open Access PDFOpenAlex
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Non-existence of co-spectral simple connected graphs with small number of edges · ArXiv.org (2025) | TGRS Research Map | TGRS