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 …

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 mutual-visibility number μ (G) …

If $ G $ is a graph and $ X\subseteq V (G) $, then $ X $ is a total mutual-visibility set if every
pair of vertices $ x $ and $ y $ of $ G $ admits a shortest $ x, y $-path $ P $ with $ V (P)\cap …

The general position problem in graphs is to find the largest possible set of vertices with the
property that no three of them lie on a common shortest path. The mutual-visibility problem in …

Given a connected graph G, the total mutual-visibility number of G, denoted μ t (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 …

Abstract The Mutual Visibility is a well-known problem in the context of mobile robots. For a
set of n robots disposed in the Euclidean plane, it asks for moving the robots without …

For a set of robots disposed on the Euclidean plane, Mutual Visibility is often desirable. The
requirement is to move robots without collisions so as to achieve a placement where no …

If $ G $ is a graph and $ X\subseteq V (G) $, then $ X $ is a total mutual-visibility set if every
pair of vertices $ x $ and $ y $ of $ G $ admits a shortest $ x, y $-path $ P $ with $ V (P)\cap …

The concept of mutual-visibility in graphs has been recently introduced. 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 …

The mutual-visibility problem in a graph G asks for the cardinality of a largest set of vertices
S⊆ V (G) so that for any two vertices x, y∈ S there is a shortest x, y-path P so that all internal …