Variety of mutual-visibility problems in hypercubes

Danilo Korže and Aleksander Vesel

Applied Mathematics and Computation, 2025, vol. 491, issue C

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.

Keywords: Mutual visibility; Hypercube; Binary code (search for similar items in EconPapers)
Date: 2025
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324006799
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:491:y:2025:i:c:s0096300324006799

DOI: 10.1016/j.amc.2024.129218

Access Statistics for this article

Applied Mathematics and Computation is currently edited by Theodore Simos

More articles in Applied Mathematics and Computation from Elsevier
Bibliographic data for series maintained by Catherine Liu ().