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A new equivalent transformation of electrical circuits with applications

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  • Cheng, Sujing
  • Ge, Jun

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.

Suggested Citation

  • Cheng, Sujing & Ge, Jun, 2026. "A new equivalent transformation of electrical circuits with applications," Chaos, Solitons & Fractals, Elsevier, vol. 209(P1).
    • Handle: RePEc:eee:chsofr:v:209:y:2026:i:p1:s0960077926006624
    DOI: 10.1016/j.chaos.2026.118521
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