On determinants of resistance matrices
arXiv:2606.21902
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.
8 pages, 2 figures. Comments welcome!