Year: 2025
Type: article
Abstract: Let d be a positive integer. The mutual d-visibility number $${\mu ^d}(G)$$ μ d ( G ) of a graph G is introduced as the cardinality of the largest mutual d-visibility set. That is, $$X\subseteq V(G)$$ X ⊆ V ( G ) is a mutual d-visibility set if for any pair of vertices $$x,y\in X$$ x , y ∈ X , the distance between them is larger than d, or there exists a shortest x, y-path in G whose internal vertices are not in X. Several combinatorial and computational aspects of $${\mu ^d}(G)$$ μ d ( G ) are given in this work. Finally, the NP-completeness of the decision problem concerning finding $${\mu ^d}(G)$$ μ d ( G ) is proved.
Source: Results in Mathematics
Authors: Dorota Kuziak, Luis P. Montejano, Juan A. Rodríguez-Velázquez
Institutions: Universidad de Cádiz, Universitat Rovira i Virgili
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: G4687697941, G745419941, G8537714269
OpenAlex ID: W4411139045