On electric resistances for distance-regular graphs

Abstract

We investigate the behavior of electric potentials on distance-regular graphs, and extend some results of a prior paper. Our main result, Theorem 4, shows(together with Corollary 3) that if distance is measured by the electric resistance between points then all points are close to being equidistant on a distance-regular graph with large valency. A number of auxiliary results are also presented.

References in corpus (2)

• Distance-regular graph with large a1 or c2
• There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2/k and large diameter