| Title: | On a generalization of median graphs: k-median graphs |
|---|
| Authors: | ID Hellmuth, Marc (Author)
ID Thekkumpadan Puthiyaveedu, Sandhya (Author) |
|---|
| Files: |  AMC_Hellmuth,Thekkumpadan_Puthiyaveedu_2025.pdf (520,78 KB)
MD5: 0CD964F4071F89B35B1242D37990B92E
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | ZUP - University of Primorska Press
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | median graph, convexity, meshed and quadrangle property, modular, interval |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 29.05.2025 |
|---|
| Publisher: | Založba Univerze na Primorskem |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | 27 str. |
|---|
| Numbering: | Vol. 25, no. 3, [article no.] P3.06 |
|---|
| PID: | 20.500.12556/RUP-22009  |
|---|
| UDC: | 519.17 |
|---|
| eISSN: | 1855-3974 |
|---|
| DOI: | https://doi.org/10.26493/1855-3974.3134.87b |
|---|
| Publication date in RUP: | 22.10.2025 |
|---|
| Views: | 237 |
|---|
| Downloads: | 0 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
