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Potential Theory on Distance-Regular Graphs

Published online by Cambridge University Press:  12 September 2008

Norman L. Biggs
Norman L. Biggs
Affiliation:
London School of Economics, Houghton St., London WC2A 2AE
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Abstract

A graph may be regarded as an electrical network in which each edge has unit resistance. We obtain explicit formulae for the effective resistance of the network when a current enters at one vertex and leaves at another in the distance-regular case. A well-known link with random walks motivates a conjecture about the maximum effective resistance. Arguments are given that point to the truth of the conjecture for all known distance-regular graphs.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 2 , Issue 3 , September 1993 , pp. 243 - 255
Copyright
Copyright © Cambridge University Press 1993

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