A Conjecture of Biggs Concerning the Resistance of a Distance-Regular Graph

摘要

Biggs conjectured that the resistance between any two points on a distance-regular graph of valency greater than 2 is bounded by twice the resistance between adjacent points. We prove this conjecture, give the sharp constant for the inequality, and display the graphs for which the conjecture most nearly fails. Some necessary background material is included, as well as some consequences.