20.500.12556/RUP-22068 On distance preserving and sequentially distance preserving graphs Grafi, ki ohranjajo razdaljo in grafi, ki zaporedno ohranjajo razdaljo 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. distance preserving isometric subgraph sequentially distance preserving chordal cut vertex simplicial vertex ohranjanje razdalje izometrični podgraf zaporedno ohranjanje razdalje tetiva izrezana točka simplicialna točka true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-11-03 11:34:48 2025-11-03 11:34:49 2025-11-18 03:04:41 0000-00-00 00:00:00 2025 0 0 10 str. no. 2, [article no.] P2.05 Vol. 8 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-03-17 519.17 2590-9770 10.26493/2590-9770.1813.5ce ADAM_Smith,Zahedi_2025.pdf ADAM_Smith,Zahedi_2025.pdf 1 BFDD4DE2A42E81AC704881B18A5EA0C9 69f58719280bb20dd457a759977f1b274964dd3481282344b4564ea581c0b525 6037cd81-b8a1-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32013 Založba Univerze na Primorskem 0 0 0