A New Proof of Foster’s First Theorem
A New Proof of Foster’s First Theorem
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DOI：
10.1080/00029890.2020.1668709
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发表时间：
2020-01
期刊：
影响因子：
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通讯作者：
Jingyuan Zhang;Weigen Yan
中科院分区：
文献类型：
--
作者：
Jingyuan Zhang;Weigen Yan
Abstract Let G be an electrical network graph with vertex set V and edge set E, and let be the effective resistance between vertices i and j of G. Foster’s first theorem states that , where cij is the conductance of the edge (i, j). In this note, we give a combinatorial proof of two equivalent formulae on the weighted enumeration of spanning trees of an edge-weighted graph, one of which results in a new proof of Foster’s first theorem.
