Volume entropy, systole and stable norm on graphs

Details Volume entropy, systole and stable norm on graphs Volume entropy, systole and stable norm on graphs

2004-11-25

arxiv.org/abs/math/0411578v2

Journal of Graph Theory 55, 4 (2007) 291-305

Mathematics

Metric Geometry

Scientific paper

10.1002/jgt.20236

We study some new isoperimetric inequalities on graphs. We etablish a
relation between the volume entropy (or asymptotic volume), the systole and the
first Betti number of weighted graphs. We also find bounds for the volume,
associated to some special measure, of the unit ball for the stable norm of
graphs.

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