RT journal article
T1 Mutual-visibility in strong products of graphs via total mutual-visibility
A1 Cicerone, Serafino
A1 Di Stefano, Gabriele
A1 Klavžar, Sandi
A1 González Yero, Ismael
A2 Matemáticas
K1 Mutual-visibility set
K1 Mutual-visibility number
K1 Total mutual-visibility set
K1 Strong product of graphs
AB Let G be a graph and X ⊆ V(G). Then X is a mutual-visibility set if each pair of vertices from X is connected by a geodesic with no internal vertex in X. The mutualvisibility number µ(G) of G is the cardinality of a largest mutual-visibility set. In this paper, the mutual-visibility number of strong product graphs is investigated. As a tool for this, total mutual-visibility sets are introduced. Along the way, basic properties of such sets are presented. The (total) mutual-visibility number of strong products is bounded from below in two ways, and determined exactly for strong grids of arbitrary dimension. Strong prisms are studied separately and a couple of tight bounds for their mutual-visibility number are given.
PB Elsevier
SN 0166-218X
YR 2024
FD 2024
LK http://hdl.handle.net/10498/35699
UL http://hdl.handle.net/10498/35699
LA eng
DS Repositorio Institucional de la Universidad de Cádiz
RD 10-may-2026