@misc{10498/35699,
year = {2024},
url = {http://hdl.handle.net/10498/35699},
abstract = {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.},
publisher = {Elsevier},
keywords = {Mutual-visibility set},
keywords = {Mutual-visibility number},
keywords = {Total mutual-visibility set},
keywords = {Strong product of graphs},
title = {Mutual-visibility in strong products of graphs via total mutual-visibility},
doi = {10.1016/J.DAM.2024.06.038},
author = {Cicerone, Serafino and Di Stefano, Gabriele and Klavžar, Sandi and González Yero, Ismael},
}