| Title: | Strong edge geodetic problem on complete multipartite graphs and some extremal graphs for the problem |
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| Authors: | ID Klavžar, Sandi (Author)
ID Zmazek, Eva (Author) |
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| Files: |  URL - Source URL, visit https://link.springer.com/article/10.1007/s41980-023-00849-6
 PDF - Presentation file, download (430,75 KB)
MD5: 9BE8331E3983B59A05BAFEBD3FB74015
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | A set of vertices $X$ of a graph $G$ is a strong edge geodetic set if to any pair of vertices from $X$ we can assign one (or zero) shortest path between them such that every edge of $G$ is contained in at least one on these paths. The cardinality of a smallest strong edge geodetic set of $G$ is the strong edge geodetic number ${\rm sg_e}(G)$ of $G$. In this paper, the strong edge geodetic number of complete multipartite graphs is determined. Graphs $G$ with ${\rm sg_e}(G) = n(G)$ are characterized and ${\rm sg_e}$ is determined for Cartesian products $P_n\,\square\, K_m$. The latter result in particular corrects an error from the literature. |
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| Keywords: | strong edge geodetic problem, complete multipartite graph, edge-coloring, Cartesian product of graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.02.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | 13 str. |
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| Numbering: | Vol. 50, iss. 1, article no. 13 |
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| PID: | 20.500.12556/DiRROS-18207  |
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| UDC: | 519.17 |
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| ISSN on article: | 1018-6301 |
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| DOI: | 10.1007/s41980-023-00849-6 |
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| COBISS.SI-ID: | 183235331 |
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| Note: |
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| Publication date in DiRROS: | 19.02.2024 |
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| Views: | 1086 |
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| Downloads: | 581 |
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