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 …

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 …

A vertex subset R of a graph G is called a general position set if any triple V 0⊆ R is non-
geodesic, this is, the three elements of V 0 do not lie on the same geodesic in G. The …

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 …

Given a graph G=(V (G), E (G)) and a set P⊆ V (G), the following concepts have been
recently introduced:(i) two elements of P are mutually visible if there is a shortest path …

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) …

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 …

A subset of vertices of a graph G is a general position set if no triple of vertices from the set
lie on a common shortest path in G. In this paper we introduce the general position …

The general position number gp (G) of a connected graph G is the cardinality of a largest set
S of vertices such that no three distinct vertices from S lie on a common geodesic; such sets …

A subset $ S $ of vertices of a graph $ G $ is a\emph {general position set} if no shortest path
in $ G $ contains three or more vertices of $ S $. In this paper, we generalise a problem of M …