| Title: | On distance preserving and sequentially distance preserving graphs |
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| Authors: | ID Smith, Jason P. (Author)
ID Zahedi, Emad (Author) |
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| Files: |  ADAM_Smith,Zahedi_2025.pdf (370,44 KB)
MD5: BFDD4DE2A42E81AC704881B18A5EA0C9
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | ZUP - University of Primorska Press
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| 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. |
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| Keywords: | distance preserving, isometric subgraph, sequentially distance preserving, chordal, cut vertex, simplicial vertex |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 17.03.2025 |
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| Publisher: | Založba Univerze na Primorskem |
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| Year of publishing: | 2025 |
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| Number of pages: | 10 str. |
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| Numbering: | Vol. 8, no. 2, [article no.] P2.05 |
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| PID: | 20.500.12556/RUP-22068  |
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| UDC: | 519.17 |
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| eISSN: | 2590-9770 |
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| DOI: | 10.26493/2590-9770.1813.5ce |
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| Publication date in RUP: | 03.11.2025 |
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| Views: | 358 |
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| Downloads: | 1 |
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