Constructs homometric non-congruent circular metric spaces (some sharing magnitude), proves regular polygons are determined by distance multiset among planar spaces but not generally, and determines magnitude uniqueness for several n-gons and n-cycles.
Leinster, The magnitude of a graph
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Distinguishing regular polygons, cycle graphs, and circular metric spaces by the distance multiset and magnitude
Constructs homometric non-congruent circular metric spaces (some sharing magnitude), proves regular polygons are determined by distance multiset among planar spaces but not generally, and determines magnitude uniqueness for several n-gons and n-cycles.