1. Note on intrinsic metrics on graphs
- Author
-
Lenz, Daniel, Schmidt, Marcel, and Seifert, Felix
- Subjects
Mathematics - Functional Analysis ,Mathematics - 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.
- Published
- 2023