A new equivalent transformation of electrical circuits with applications

Sujing Cheng and Jun Ge

Chaos, Solitons & Fractals, 2026, vol. 209, issue P1

Abstract: We introduce a new equivalent transformation of electrical circuits called the vertex-weighted complete multipartite graph-blossomed star transformation. This transformation generalizes previous results by incorporating vertex weights, enabling the analysis of heterogeneous networks. As applications, we derive explicit closed-form expressions for resistance distances and for the sum of weights of spanning trees in vertex-weighted complete multipartite graphs plus a matching. Furthermore, we use the transformation to establish counting formulas for spanning trees in vertex-weighted almost complete s-partite graphs, obtaining explicit combinatorial expressions for the cases 2≤s≤4.

Keywords: Vertex-weighted complete multipartite graph; Resistance distance; Spanning tree; Equivalent transformation of electrical circuits (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926006624

DOI: 10.1016/j.chaos.2026.118521

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