Express the number of spanning trees in term of degrees

Fengming Dong, Jun Ge and Zhangdong Ouyang

Applied Mathematics and Computation, 2022, vol. 415, issue C

Abstract: It is well-known that the number of spanning trees, denoted by τ(G), in a connected multi-graph G can be calculated by the Matrix-Tree Theorem and Tutte’s deletion-contraction formula. In this short note, we find an alternate method to compute τ(G) by degrees of vertices.

Keywords: Spanning tree; Degree; Graph polynomial (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:415:y:2022:i:c:s0096300321007815

DOI: 10.1016/j.amc.2021.126697

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