| Title: | Variety of mutual-visibility problems in hypercubes |
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| Authors: | ID Korže, Danilo (Author)
ID Vesel, Aleksander (Author) |
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| Files: |  1-s2.0-S0096300324006799-main.pdf (571,90 KB)
MD5: FB666CEAEF7E2F57429750877F8A6CA1
 https://www.sciencedirect.com/science/article/pii/S0096300324006799?via%3Dihub#dav0001
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| Language: | English |
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| Work type: | Article |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FERI - Faculty of Electrical Engineering and Computer Science
FNM - Faculty of Natural Sciences and Mathematics
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| Abstract: | Let G be a graph and M ⊆ V(G). Vertices x, y ∈ M are M-visible if there exists a shortest x, y-path of G that does not pass through any vertex of M ⧵ {x, y}. We say that M is a mutual-visibility set if each pair of vertices of M is M-visible, while the size of any largest mutual-visibility set of G is the mutual-visibility number of G. If some additional combinations for pairs of vertices x, y are required to be M-visible, we obtain the total (every x, y ∈ V (G) are M-visible), the outer (every x ∈ M and every y ∈ V (G) ⧵ M are M-visible), and the dual (every x, y ∈ V (G) ⧵ M are M-visible) mutual-visibility set of G. The cardinalities of the largest of the above defined sets are known as the total, the outer, and the dual mutual-visibility number of G, respectively. We present results on the variety of mutual-visibility problems in hypercubes. |
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| Keywords: | mutual visibility, hypercube, binary code |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Submitted for review: | 14.05.2024 |
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| Article acceptance date: | 23.11.2024 |
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| Publication date: | 02.12.2024 |
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| Publisher: | Elsevier |
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| Year of publishing: | 2025 |
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| Number of pages: | 10 str. |
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| Numbering: | Vol. 491, št. članka 129218 |
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| PID: | 20.500.12556/DKUM-91779  |
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| UDC: | 51 |
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| ISSN on article: | 1873-5649 |
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| COBISS.SI-ID: | 217980931 |
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| DOI: | 10.1016/j.amc.2024.129218 |
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| Copyright: | © 2024 The Author(s). |
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| Publication date in DKUM: | 04.02.2025 |
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| Views: | 148 |
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| Downloads: | 12 |
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| Metadata: |    |
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| Categories: | Misc.
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