On the critical group of the k-partite graph
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929486112489472 |
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| author | Dong, Xinyu Jiang, Guangfeng Guo, Weili |
| author_facet | Dong, Xinyu Jiang, Guangfeng Guo, Weili |
| contents | The critical group of a connected graph is closely related to the graph Laplacian, and is of high research value in combinatorics, algebraic geometry, statistical physics, and several other areas of mathematics. In this paper, we study the k-partite graphs and introduce an algorithm to get the structure of their critical groups by calculating the Smith normal forms of their graph Laplacians. When k is from 2 to 6, we characterize the structure of the critical groups completely, which can generalize the results of the complete bipartite graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_02654 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the critical group of the k-partite graph Dong, Xinyu Jiang, Guangfeng Guo, Weili Combinatorics 05C50, 20K01 The critical group of a connected graph is closely related to the graph Laplacian, and is of high research value in combinatorics, algebraic geometry, statistical physics, and several other areas of mathematics. In this paper, we study the k-partite graphs and introduce an algorithm to get the structure of their critical groups by calculating the Smith normal forms of their graph Laplacians. When k is from 2 to 6, we characterize the structure of the critical groups completely, which can generalize the results of the complete bipartite graphs. |
| title | On the critical group of the k-partite graph |
| topic | Combinatorics 05C50, 20K01 |
| url | https://arxiv.org/abs/2409.02654 |