Counting spanning hypertrees in non-uniform hypergraphs based on sum operation

Ke Zhang (), Jiachun Guo, Lixin Dong () and Hongwei Yin ()
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Ke Zhang: School of Information Engineering, Huzhou University, Huzhou 313000, Zhejiang, P. R. China
Jiachun Guo: ��School of Humanities, Huzhou College, Huzhou 313000, Zhejiang, P. R. China
Lixin Dong: ��School of Computer, Qinghai Normal University, Xining 810800, P. R. China
Hongwei Yin: School of Information Engineering, Huzhou University, Huzhou 313000, Zhejiang, P. R. China

International Journal of Modern Physics C (IJMPC), 2024, vol. 35, issue 04, 1-15

Abstract: The theoretical and applied research on hypergraph or hypernetwork is one of the hot topics of system science. Spanning hypertree extended from spanning tree is an interesting problem about this topic, but determining the number of spanning hypertrees in general hypergraphs is not suitable for generalizing from graph and more intractable. In this paper, we propose a definition of spanning hypertree which has less constraints than the traditional definition of spanning hypertree, and then find exact analytical expressions for the number of spanning hypertrees in several kinds of non-uniform hypergraphs based on sum operation. In addition, we define the entropy of spanning hypertree and conduct data experiments on the entropies of spanning hypertrees in four special classes of non-uniform hypergraphs.

Keywords: Non-uniform hypergraph; the number of spanning hypertrees; the entropy of spanning hypertree (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0129183124500426

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