Abstract A [1, 2]-set of a graph G is a set S of vertices of G if every vertex not in S has one or
two neighbors in S. The [1, 2]-domination number γ [1, 2](G) of G equals the minimum …

In 2013 the concept of [j, k]-dominating sets in graphs have been introduced as an extension
of [1, k]-dominating sets. Regarding studying [j, k]-dominating sets, the research is also …

For positive integers j and k with j≤ k, a subset S⊆ V in a graph G=(V, E) is a [j, k]-set if
every vertex in VS is adjacent to at least j vertices in S but no more than k vertices in S. The …

A subset $ D $ of the vertex set $ V $ of a graph $ G $ is called an $[1, k] $-dominating set if
every vertex from $ VD $ is adjacent to at least one vertex and at most $ k $ vertices of $ D …

A set S of vertices of a graph G is a geodesic transversal of G if every maximal geodesic of G
contains at least one vertex of S. The minimum cardinality of a geodesic transversal of G is …