A dominating set of a graph is a set S of vertices such that every vertex in the graph is either
in S or is adjacent to a vertex in S. The domination number of a graph G, denoted γ (G), is …

A dominating set D⊂ V of a graph G is a set such that each vertex v∈ V is either in the set or
adjacent to a vertex in the set. We show that if G is an n-vertex maximal outerplanar graph …

We show that every planar triangulation on n> 10 vertices has a dominating set of size 2
n/7= n/3.5. This approaches the n/4 bound conjectured by Matheson and Tarjan [12], and …

Abstract A set R⊆ V (G) of a graph G is a general position set if any triple set R 0 of R is non-
geodesic, that is, no vertex of R 0 lies on any geodesic between the other two vertices of R 0 …

Abstract A set D⊆ V (G) of a graph G is a dominating set if every vertex v∈ V (G) is either in
D or adjacent to a vertex in D. The domination number γ (G) of a graph G is the minimum …

We introduce a class of plane graphs called weak near-triangulations, and prove that this
class is closed under certain graph operations. Then we use the properties of weak near …

The minimum dominating set (MDS) problem is a fundamental subject of theoretical
computer science, and has found vast applications in different areas, including sensor …

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Let G be a graph and γ (G) denote the domination number of G, ie the cardinality of a
smallest set of vertices S such that every vertex of G is either in S or adjacent to a vertex in S …

Abstract In 1996, Tarjan and Matheson proved that if G is a plane triangulated disc with n
vertices, γ (G)≤ n/3, where γ (G) denotes the domination number of G, ie the cardinality of …