Note on intrinsic metrics on graphs
Functional Analysis
2023-08-25 v1 Metric Geometry
Abstract
We study the set of intrinsic metrics on a given graph. This is a convex compact set and it carries a natural order. We investigate existence of largest elements with respect to this order. We show that the only locally finite graphs which admit a largest intrinsic metric are certain finite star graphs. In particular all infinite locally finite graphs do not admit a largest intrinsic metric. Moreover, we give a characterization for the existence of intrinsic metrics with finite balls for weakly spherically symmetric graphs.
Keywords
Cite
@article{arxiv.2308.12665,
title = {Note on intrinsic metrics on graphs},
author = {Daniel Lenz and Marcel Schmidt and Felix Seifert},
journal= {arXiv preprint arXiv:2308.12665},
year = {2023}
}