A collection of results concerning electric resistance and simple random walk on distance-regular graphs

In this paper, we prove a number of related results on distance-regular graphs concerning electric resistance and simple random walk. We begin by proving several results on electric resistance; in particular we prove a sharp constant bounding the ratio of electrical resistances between any two pairs of points and give a counterexample to a conjecture made in a previous paper regarding the growth of resistances with respect to distance. We then show how a number of strong bounds on moments of hitting times, cover times, and related quantities for simple random walk may be deduced from the bound on resistance.