Volume entropy, systole and stable norm on graphs

Florent N. Balacheff (1)

1 LPP - Laboratoire Paul Painlevé - UMR 8524

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.

Mots clés: graph; volume entropy; systole; stable norm

Domaines: Géométrie métrique [math.MG]; Combinatoire [math.CO]

Florent N. Balacheff. Volume entropy, systole and stable norm on graphs. Journal of Graph Theory, 2007, 55 (4), pp.291-305. ⟨10.1002/jgt.20236⟩. ⟨hal-00003351v2⟩