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arXiv · 2409.02654

On the critical group of the k-partite graph

Xinyu Dong·Guangfeng Jiang·Weili Guo
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Abstract

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.

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Xinyu Dong, Guangfeng Jiang, Weili Guo. 2024-09-04. On the critical group of the k-partite graph. https://arxiv.org/abs/2409.02654

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