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arXiv · 2606.21902

On determinants of resistance matrices

Harry Richman·Farbod Shokrieh·Chenxi Wu
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Abstract

We prove a new combinatorial identity for the determinant of the resistance matrix of a finite graph, which involves counts of spanning trees and forests. This generalizes a result of Graham and Pollak on distances matrices of trees. We make use of Bapat's expression of the resistance matrix determinant as a linear algebraic quantity.

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Harry Richman, Farbod Shokrieh, Chenxi Wu. 2026-06-20. On determinants of resistance matrices. https://arxiv.org/abs/2606.21902

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