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On distance preserving and sequentially distance preserving graphsJason P. Smith,
Emad Zahedi, 2025, original scientific article
Abstract: A graph H is an isometric subgraph of G if d_H(u,v)=d_G(u,v), for every pair u,v ∈ V(H). A graph is distance preserving if it has an isometric subgraph of every possible order. A graph is sequentially distance preserving if its vertices can be ordered such that deleting the first i vertices results in an isometric subgraph, for all i≥1. We give an equivalent condition to sequentially distance preserving based upon simplicial orderings. Using this condition, we prove that if a graph does not contain any induced cycles of length 5 or greater, then it is sequentially distance preserving and thus distance preserving. Next we consider the distance preserving property on graphs with a cut vertex. Finally, we define a family of non-distance preserving graphs constructed from cycles.
Keywords: distance preserving, isometric subgraph, sequentially distance preserving, chordal, cut vertex, simplicial vertex
Published in RUP: 03.11.2025; Views: 437; Downloads: 2
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