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Research Article | Open Access

Laplacian integral signed graphs with few cycles

Dijian Wang1, Dongdong Gao2( )
School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, China
Department of Mathematics and Computer Science, Tongling University, Tongling, Anhui 244000, China
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Abstract

A connected graph with n vertices and m edges is called k-cyclic graph if k = m − n + 1. We call a signed graph is Laplacian integral if all eigenvalues of its Laplacian matrix are integers. In this paper, we will study the Laplacian integral k-cyclic signed graphs with k = 0 , 1 , 2 , 3 and determine all connected Laplacian integral signed trees, unicyclic, bicyclic and tricyclic signed graphs.

Keywords

signed graphLaplacian integral graphspectrum
CLC number: 05C50, 05C22

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AIMS Mathematics
Volume 8 Issue 3,
March 2023
Pages 7021-7031
DOI: 10.3934/math.2023354

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Cite this article:
Wang D, Gao D. Laplacian integral signed graphs with few cycles. AIMS Mathematics, 2023, 8(3): 7021-7031. https://doi.org/10.3934/math.2023354

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Received: 25 October 2022
Revised: 27 December 2022
Accepted: 03 January 2023
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)