A toll walk W= w 1⋯ wk in a graph G is a walk in which w 1 is adjacent only to w 2 and wk is
adjacent only to wk-1 among all vertices of W. The toll walk interval T (u, v) between u, v∈ V …

In this paper we introduce the notion of l k-convexity, a natural restriction of the monophonic
convexity. Let G be a graph and k≥ 2 an integer. A subset S⊆ V (G) is l k-convex if and only …

Graph convexity has been used as an important tool to better understand the structure of
classes of graphs. Many studies are devoted to determine if a graph equipped with a …

A walk u0, u1,..., uk− 1, uk in a graph G is a weakly toll walk if u0ui∈ E (G) implies ui= u1
and uj uk∈ E (G) implies uj= uk− 1. A set S of vertices of G is weakly toll convex if for any two …

We study half-space separation in the convexity of chordless paths of a graph, ie,
monophonic convexity. In this problem, one is given a graph and two (disjoint) subsets of …

A tolled walk T between two different, non-adjacent vertices u, v in a graph G is a walk in
which u and v have exactly one neighbor. A toll interval between u, v∈ V (G), T (u, v), is the …

We study domination between different types of walks connecting two non-adjacent vertices
u and v of a graph (shortest paths, induced paths, paths, tolled walks). We succeeded in …

Toll walks on connected graphs are introduced to characterize dominating pairs of vertices
in interval graphs. A weak-toll walk is an immediate generalization of a toll walk in a graph …

A tolled walk T between two non-adjacent vertices u and v in a graph G is a walk, in which u
is adjacent only to the second vertex of T and v is adjacent only to the second-to-last vertex …

In this paper we prove some bounds for Steiner distance in Cartesian product. We
investigate properties of connected subgraphs that are not Steiner convex. Those results are …