| Title: | Mutual-visibility in strong products of graphs via total mutual-visibility |
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| Authors: | ID Cicerone, Serafino (Author)
ID Di Stefano, Gabriele (Author)
ID Klavžar, Sandi (Author)
ID Yero, Ismael G. (Author) |
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| Files: |  PDF - Presentation file, download (618,95 KB)
MD5: 9F622F07C0DA768E2A9136C1680C2F92
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0166218X24002907
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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: | Let $G$ be a graph and $X\subseteq V(G)$. Then $X$ is a mutual-visibility set if each pair of vertices from $X$ is connected by a geodesic with no internal vertex in $X$. The mutual-visibility number $\mu(G)$ of $G$ is the cardinality of a largest mutual-visibility set. In this paper, the mutual-visibility number of strong product graphs is investigated. As a tool for this, total mutual-visibility sets are introduced. Along the way, basic properties of such sets are presented. The (total) mutual-visibility number of strong products is bounded from below in two ways, and determined exactly for strong grids of arbitrary dimension. Strong prisms are studied separately and a couple of tight bounds for their mutual-visibility number are given. |
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| Keywords: | mutual-visibility set, mutual-visibility number, total mutual-visibility set, strong 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: | 01.12.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 136-146 |
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| Numbering: | Vol. 358 |
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| PID: | 20.500.12556/DiRROS-20505  |
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| UDC: | 519.17 |
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| ISSN on article: | 0166-218X |
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| DOI: | 10.1016/j.dam.2024.06.038 |
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| COBISS.SI-ID: | 201822467 |
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| Note: |
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| Publication date in DiRROS: | 02.10.2024 |
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| Views: | 8 |
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| Downloads: | 5 |
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