Laplacian integral signed graphs with few cycles
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 connec...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023354?viewType=HTML |
| _version_ | 1797936913489854464 |
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| author | Dijian Wang Dongdong Gao |
| author_facet | Dijian Wang Dongdong Gao |
| author_sort | Dijian Wang |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T18:36:39Z |
| format | Article |
| id | doaj.art-b6407321d31e4b899966ad8b198b8f91 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T18:36:39Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-b6407321d31e4b899966ad8b198b8f912023-02-02T01:10:59ZengAIMS PressAIMS Mathematics2473-69882023-01-01837021703110.3934/math.2023354Laplacian integral signed graphs with few cyclesDijian Wang0Dongdong Gao11. School of Science, Zhejiang University of Science and Technology, Hangzhou, Zhejiang, 310023, China2. Department of Mathematics and Computer Science, Tongling University, Tongling, Anhui 244000, ChinaA 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.https://www.aimspress.com/article/doi/10.3934/math.2023354?viewType=HTMLsigned graphlaplacian integral graphspectrum |
| spellingShingle | Dijian Wang Dongdong Gao Laplacian integral signed graphs with few cycles AIMS Mathematics signed graph laplacian integral graph spectrum |
| title | Laplacian integral signed graphs with few cycles |
| title_full | Laplacian integral signed graphs with few cycles |
| title_fullStr | Laplacian integral signed graphs with few cycles |
| title_full_unstemmed | Laplacian integral signed graphs with few cycles |
| title_short | Laplacian integral signed graphs with few cycles |
| title_sort | laplacian integral signed graphs with few cycles |
| topic | signed graph laplacian integral graph spectrum |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023354?viewType=HTML |
| work_keys_str_mv | AT dijianwang laplacianintegralsignedgraphswithfewcycles AT dongdonggao laplacianintegralsignedgraphswithfewcycles |