Maximum hitting time for random walks on graphs

Authors:
Graham Brightwell;Peter Winkler
Affiliations:
Cambridge University, Cambridge, United Kingdom;Emory University, Atlanta, GA, and Bellcore, Morristown, NJ
Venue:
Random Structures & Algorithms
Year:
1990

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Abstract

For x and y vertices of a connected graph G, let TG(x, y) denote the expected time before a random walk starting from x reaches y. We determine, for each n 0, the n‐vertex graph G and vertices x and y for which TG(x, y) is maximized. the extremal graph consists of a clique on ⌊(2n + 1)/3⌋) (or ⌈)(2n − 2)/3⌉) vertices, including x, to which a path on the remaining vertices, ending in y, has been attached; the expected time TG(x, y) to reach y from x in this graph is approximately 4n3/27. © 1990 Wiley Periodicals, Inc.