Further results on permanents of Laplacian matrices of trees
The research on the permanents of graph matrices is one of the contemporary research topic in algebraic combinatorics. Brualdi and Goldwasser characterized the upper and lower bounds of permanents of Laplacian matrices of trees. In this article, we determined the second and third minimal permanents...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-08-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0185 |
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| _version_ | 1849390269567336448 |
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| author | Wu Tingzeng Dong Xiangshuai |
| author_facet | Wu Tingzeng Dong Xiangshuai |
| author_sort | Wu Tingzeng |
| collection | DOAJ |
| description | The research on the permanents of graph matrices is one of the contemporary research topic in algebraic combinatorics. Brualdi and Goldwasser characterized the upper and lower bounds of permanents of Laplacian matrices of trees. In this article, we determined the second and third minimal permanents of the Laplacian matrices of trees, and the second maximal permanent of the Laplacian matrices of trees is given. The corresponding extremal graphs are characterized. Furthermore, we determined bounds of permanents of the Laplacian matrices of non-caterpillar trees with given graph parameters. Moreover, the corresponding extremal graphs are determined. |
| format | Article |
| id | doaj-art-8fff92cfddf74fd2a0f2a3d72394cd57 |
| institution | Kabale University |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-8fff92cfddf74fd2a0f2a3d72394cd572025-08-20T03:41:43ZengDe GruyterOpen Mathematics2391-54552025-08-0123118920110.1515/math-2025-0185Further results on permanents of Laplacian matrices of treesWu Tingzeng0Dong Xiangshuai1School of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810007, P. R. ChinaSchool of Mathematics and Statistics, Qinghai Nationalities University, Xining, Qinghai 810007, P. R. ChinaThe research on the permanents of graph matrices is one of the contemporary research topic in algebraic combinatorics. Brualdi and Goldwasser characterized the upper and lower bounds of permanents of Laplacian matrices of trees. In this article, we determined the second and third minimal permanents of the Laplacian matrices of trees, and the second maximal permanent of the Laplacian matrices of trees is given. The corresponding extremal graphs are characterized. Furthermore, we determined bounds of permanents of the Laplacian matrices of non-caterpillar trees with given graph parameters. Moreover, the corresponding extremal graphs are determined.https://doi.org/10.1515/math-2025-0185treenon-caterpillar treelaplacian matrixpermanentgraph parameter05c5005c0515a15 |
| spellingShingle | Wu Tingzeng Dong Xiangshuai Further results on permanents of Laplacian matrices of trees Open Mathematics tree non-caterpillar tree laplacian matrix permanent graph parameter 05c50 05c05 15a15 |
| title | Further results on permanents of Laplacian matrices of trees |
| title_full | Further results on permanents of Laplacian matrices of trees |
| title_fullStr | Further results on permanents of Laplacian matrices of trees |
| title_full_unstemmed | Further results on permanents of Laplacian matrices of trees |
| title_short | Further results on permanents of Laplacian matrices of trees |
| title_sort | further results on permanents of laplacian matrices of trees |
| topic | tree non-caterpillar tree laplacian matrix permanent graph parameter 05c50 05c05 15a15 |
| url | https://doi.org/10.1515/math-2025-0185 |
| work_keys_str_mv | AT wutingzeng furtherresultsonpermanentsoflaplacianmatricesoftrees AT dongxiangshuai furtherresultsonpermanentsoflaplacianmatricesoftrees |