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arXiv · 2308.12665

Note on intrinsic metrics on graphs

Daniel Lenz·Marcel Schmidt·Felix Seifert
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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.

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Daniel Lenz, Marcel Schmidt, Felix Seifert. 2023-08-24. Note on intrinsic metrics on graphs. https://arxiv.org/abs/2308.12665

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