Variety of mutual-visibility problems in graphs

If X is a subset of vertices of a graph G, then vertices u and v are X-visible if there exists a shortest u,v-path P such that V(P)∩X⊆{u,v}. If each two vertices from X are X-visible, then X is a mutual-visibility set. The mutual-visibility number of G is the cardinality of a largest mutual-visibili...

Celý popis

Uložené v:
Podrobná bibliografia
Vydané v:Theoretical computer science Ročník 974; s. 114096
Hlavní autori: Cicerone, Serafino, Di Stefano, Gabriele, Drožđek, Lara, Hedžet, Jaka, Klavžar, Sandi, Yero, Ismael G.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier B.V 29.09.2023
Predmet:
Computational complexity
Dual mutual-visibility number
Grid graph
Mutual-visibility
Outer mutual-visibility
Torus graph
Total mutual-visibility
Total mutual-visibility
Mutual-visibility
Dual mutual-visibility number
Grid graph
Torus graph
Computational complexity
Outer mutual-visibility
ISSN:0304-3975
On-line prístup:Získať plný text
Tagy: Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
Popis
Shrnutí:If X is a subset of vertices of a graph G, then vertices u and v are X-visible if there exists a shortest u,v-path P such that V(P)∩X⊆{u,v}. If each two vertices from X are X-visible, then X is a mutual-visibility set. The mutual-visibility number of G is the cardinality of a largest mutual-visibility set of G and has been already investigated. In this paper a variety of mutual-visibility problems is introduced based on which natural pairs of vertices are required to be X-visible. This yields the total, the dual, and the outer mutual-visibility numbers. We first show that these graph invariants are related to each other and to the classical mutual-visibility number, and then we prove that the three newly introduced mutual-visibility problems are computationally difficult. According to this result, we compute or bound their values for several graphs classes that include for instance grid graphs and tori. We conclude the study by presenting some inter-comparison between the values of such parameters, which is based on the computations we made for some specific families.
ISSN:0304-3975
DOI:10.1016/j.tcs.2023.114096