A conjecture of Biggs concerning the resistance of a distance-regular graph

Details A conjecture of Biggs concerning the resistance of a distance-regular graph A conjecture of Biggs concerning the resistance of a distance-regular graph

2010-06-14

arxiv.org/abs/1006.2687v1

Electronic Journal of Combinatorics, Vol. 17(1), 2010

Mathematics

Combinatorics

Scientific paper

Previously, Biggs has 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.

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