Mutual and total mutual visibility in hypercube-like graphs

Serafino Cicerone, Alessia Di Fonso, Gabriele Di Stefano, Alfredo Navarra and Francesco Piselli

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

Abstract: Let G be a graph and X⊆V(G). Then, vertices x and y of G are X-visible if there exists a shortest x,y-path where no internal vertices belong to X. The set X is a mutual-visibility set of G if every two vertices of X are X-visible, while X is a total mutual-visibility set if any two vertices from V(G) are X-visible. The cardinality of a largest mutual-visibility set (resp. total mutual-visibility set) is the mutual-visibility number (resp. total mutual-visibility number) μ(G) (resp. μt(G)) of G. It is known that computing μ(G) is an NP-complete problem, as well as μt(G). In this paper, we study the (total) mutual-visibility in hypercube-like networks (namely, hypercubes, Fibonacci cubes, cube-connected cycles, and butterflies). Concerning computing μ(G), we provide approximation algorithms for hypercubes, Fibonacci cubes and cube-connected cycles, while we give an exact formula for butterflies. Concerning computing μt(G) (in the literature, already studied in hypercubes), whereas we obtain exact formulae for both cube-connected cycles and butterflies.

Keywords: Mutual visibility; Hypercube; Fibonacci cubes; Cube-connected cycle; Butterfly; Approximation algorithm (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0096300324006775
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:s0096300324006775

DOI: 10.1016/j.amc.2024.129216

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 ().