| Naslov: | On a generalization of median graphs: k-median graphs |
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| Avtorji: | ID Hellmuth, Marc (Avtor)
ID Thekkumpadan Puthiyaveedu, Sandhya (Avtor) |
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| Datoteke: |  AMC_Hellmuth,Thekkumpadan_Puthiyaveedu_2025.pdf (520,78 KB)
MD5: 0CD964F4071F89B35B1242D37990B92E
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| Jezik: | Angleški jezik |
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| Vrsta gradiva: | Članek v reviji |
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| Tipologija: | 1.01 - Izvirni znanstveni članek |
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| Organizacija: | ZUP - Založba Univerze na Primorskem
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| Opis: | Median graphs are connected graphs in which for all three vertices there is a unique vertex that belongs to shortest paths between each pair of these three vertices. To be more formal, a graph G is a median graph if, for all μ, u, v ∈ V(G), it holds that |I(μ, u) ∩ I(μ, v) ∩ I(u, v)| = 1 where I(x, y) denotes the set of all vertices that lie on shortest paths connecting x and y.
In this paper we are interested in a natural generalization of median graphs, called k-median graphs. A graph G is a k-median graph, if there are k vertices μ1, …, μk ∈ V(G) such that, for all u, v ∈ V(G), it holds that |I(μ_i, u) ∩ I(μ_i, v) ∩ I(u, v)| = 1, 1 ≤ i ≤ k. By definition, every median graph with n vertices is an n-median graph. We provide several characterizations of k-median graphs that, in turn, are used to provide many novel characterizations of median graphs. |
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| Ključne besede: | median graph, convexity, meshed and quadrangle property, modular, interval |
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| Status publikacije: | Objavljeno |
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| Verzija publikacije: | Objavljena publikacija |
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| Datum objave: | 29.05.2025 |
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| Založnik: | Založba Univerze na Primorskem |
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| Leto izida: | 2025 |
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| Št. strani: | 27 str. |
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| Številčenje: | Vol. 25, no. 3, [article no.] P3.06 |
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| PID: | 20.500.12556/RUP-22009  |
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| UDK: | 519.17 |
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| eISSN: | 1855-3974 |
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| DOI: | https://doi.org/10.26493/1855-3974.3134.87b |
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| Datum objave v RUP: | 22.10.2025 |
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| Število ogledov: | 239 |
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| Število prenosov: | 0 |
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| Metapodatki: |    |
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