Arandomhierarchical Lattice: the Series-parallel Graph and Its Properties
نویسندگان
چکیده
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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تاریخ انتشار 2004