Simplified results on the regularity of electric resistance on a distance-regular graph

TL;DR

This paper simplifies previous results on electric resistance in distance-regular graphs, establishing bounds on resistance between points and providing easier proofs under weaker conditions.

Contribution

It offers simplified proofs and bounds for electric resistance in distance-regular graphs, improving understanding of their resistance properties.

Findings

Max resistance between points is at most twice the resistance between neighbors

Simplified proof techniques are introduced for resistance bounds

Results extend previous work with more accessible proofs

Abstract

Simplifications of a result from a prior paper concerning the electric resistance between points in a distance-regular graph are given. In particular, we prove that the maximal resistance between points is bounded by twice the resistance between neighbors. We also show that if the constant is weakened, then a very simple proof can be given.