| Title: | Variety of mutual-visibility problems in graphs |
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| Authors: | ID Cicerone, Serafino (Author)
ID Di Stefano, Gabriele (Author)
ID Drožđek, Lara (Author)
ID Hedžet, Jaka (Author)
ID Klavžar, Sandi (Author)
ID Yero, Ismael G. (Author) |
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| Files: |  PDF - Presentation file, download (456,36 KB)
MD5: 02946E0363BE3E74B415BF7F23B898C6
 URL - Source URL, visit https://www.sciencedirect.com/science/article/pii/S0304397523004097
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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: | If $X$ is a subset of vertices of a graph $G$, then vertices $u$ and $v$ are $X$-visible if there exists a shortest $u,v$-path $P$ such that $V(P)\cap X \subseteq \{u,v\}$. If each two vertices from $X$ are $X$-visible, then $X$ is a mutual-visibility set. The mutual-visibility number of $G$ is the cardinality of a largest mutual-visibility set of $G$ and has been already investigated. In this paper a variety of mutual-visibility problems is introduced based on which natural pairs of vertices are required to be $X$-visible. This yields the total, the dual, and the outer mutual-visibility numbers. We first show that these graph invariants are related to each other and to the classical mutual-visibility number, and then we prove that the three newly introduced mutual-visibility problems are computationally difficult. According to this result, we compute or bound their values for several graphs classes that include for instance grid graphs and tori. We conclude the study by presenting some inter-comparison between the values of such parameters, which is based on the computations we made for some specific families. |
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| Keywords: | mutual-visibility, total mutual-visibility, dual mutual-visibility number, outer mutual-visibility, grid graphs, torus graphs, computational complexity |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.09.2023 |
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| Year of publishing: | 2023 |
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| Number of pages: | 13 str. |
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| Numbering: | Vol. 974, art. no. ǂ114096 |
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| PID: | 20.500.12556/DiRROS-18649  |
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| UDC: | 519.17 |
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| ISSN on article: | 0304-3975 |
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| DOI: | 10.1016/j.tcs.2023.114096 |
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| COBISS.SI-ID: | 161787907 |
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| Note: | Soavtorji: Gabriele Di Stefano, Lara Drožđek, Jaka Hedžet, Sandi Klavžar, Ismael G. Yero;
Spletna objava: 6. 8. 2023;
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| Publication date in DiRROS: | 10.04.2024 |
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| Views: | 81 |
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| Downloads: | 43 |
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