Year: 2024
Type: article
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. For infinite graphs which are not locally finite the set of intrinsic metrics may be trivial as we show by an example. Moreover, we give a characterization for the existence of intrinsic metrics with finite balls for weakly spherically symmetric graphs.
Source: Mathematische Nachrichten
Authors: Daniel Lenz, Marcel Schmidt, Felix Seifert
Institutions: Friedrich Schiller University Jena, Leipzig University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Deutsche Forschungsgemeinschaft
Awards: G2290616477, G4111005476, G8715980015
OpenAlex ID: W4402658486