RT journal article
T1 Total Mutual-Visibility in Graphs with Emphasis on Lexicographic and Cartesian Products
A1 Kuziak, Dorota
A1 Rodríguez Velázquez, Juan A.
A2 Estadística e Investigación Operativa
K1 Cartesian product
K1 lexicographic product
K1 Mutual-visibility
K1 Total mutual-visibility number
K1 Total mutual-visibility set
AB Given a connected graph G, the total mutual-visibility number of G, denoted μt(G) , is the cardinality of a largest set S⊆ V(G) such that for every pair of vertices x, y∈ V(G) there is a shortest x, y-path whose interior vertices are not contained in S. Several combinatorial properties, including bounds and closed formulae, for μt(G) are given in this article. Specifically, we give several bounds for μt(G) in terms of the diameter, order and/or connected domination number of G and show characterizations of the graphs achieving the limit values of some of these bounds. We also consider those vertices of a graph G that either belong to every total mutual-visibility set of G or does not belong to any of such sets, and deduce some consequences of these results. We determine the exact value of the total mutual-visibility number of lexicographic products in terms of the orders of the factors, and the total mutual-visibility number of the first factor in the product. Finally, we give some bounds and closed formulae for the total mutual-visibility number of Cartesian product graphs.
PB Springer
SN 0126-6705
YR 2023
FD 2023-10-16
LK http://hdl.handle.net/10498/31379
UL http://hdl.handle.net/10498/31379
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026