A random hierarchical lattice: the series-parallel graph and its properties-Reference-Cited by-同舟云学术

A random hierarchical lattice: the series-parallel graph and its properties

Published:2004-09 Issue:3 Volume:36 Page:824-838
ISSN:0001-8678
Container-title:Advances in Applied Probability
language:en
Short-container-title:Advances in Applied Probability

Author:

Hambly B. M.,Jordan Jonathan

Abstract

We consider a sequence of random graphs constructed by a hierarchical procedure. The construction replaces existing edges by pairs of edges in series or parallel with probability p. We investigate the effective resistance across the graphs, first-passage percolation on the graphs and the Cheeger constants of the graphs as the number of edges tends to infinity. In each case we find a phase transition at

Publisher

Cambridge University Press (CUP)

Subject

Applied Mathematics,Statistics and Probability

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