Name: On the Critical Group of the K-Partite Graph
Keywords: 05C50, 20K01, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2024Embargo end date: 01 Jan 2024Publisher:Elsevier BV

Authors: Dong, Xinyu; Jiang, Guangfeng; Guo, Weili;

doi: 10.2139/ssrn.4880404 , 10.48550/arxiv.2409.02654

arXiv: 2409.02654

On the Critical Group of the K-Partite Graph

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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.

19 pages, 1 figure

Keywords

05C50, 20K01, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO)

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