20.500.12556/DKUM-91779 Variety of mutual-visibility problems in hypercubes 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. mutual visibility hypercube binary code vzajemna pepeoznavnost hiperkocka binarne kode true false true Elsevier Angleški jezik Slovenski jezik https://www.sciencedirect.com/journal/applied-mathematics-and-computation © 2024 The Author(s). Članek v reviji 2025-02-04 13:46:14 2025-02-04 13:46:14 2026-01-19 08:21:06 0000-00-00 00:00:00 2025 0 0 10 str. Vol. 491, št. članka 129218 15 April 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 2024-05-14 2024-11-23 2024-12-02 51 217980931 10.1016/j.amc.2024.129218 1873-5649 1-s2.0-S0096300324006799-main.pdf 1-s2.0-S0096300324006799-main.pdf 1 FB666CEAEF7E2F57429750877F8A6CA1 b7830a2b1da6fd12a6892ee334c7837b3a061b1d234df4aa926ba8fba1e82c45 64d6209c-e2f6-11ef-ba28-00155d000105 https://dk.um.si/Dokument.php?lang=slv&id=188453 https://www.sciencedirect.com/science/article/pii/S0096300324006799?via%3Dihub#dav0001 0 8da97c04-f506-11f0-94a4-00155d580e02 https://dk.um.si/Dokument.php?lang=slv&id=202139 Fakulteta za elektrotehniko, računalništvo in informatiko Fakulteta za naravoslovje in matematiko 0 0 0