Journal article

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

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 $p$ and $1-p$ respectively. 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 $p=1/2$.

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Publication date:
2003-01-01
UUID:
uuid:cc9881d6-d2b0-4001-996a-71db04bcea4a
Local pid:
oai:eprints.maths.ox.ac.uk:112
Deposit date:
2011-05-19