For an integer $ k\ge 1$, a (distance) $ k $-dominating set of a connected graph $ G $ is a
set $ S $ of vertices of $ G $ such that every vertex of $ V (G)\setminus S $ is at distance at …

DOMINATION INTEGRITY IN TREES Page 1 BULLETIN OF INTERNATIONAL MATHEMATICAL
VIRTUAL INSTITUTE ISSN 1840-4367 Vol. 2(2012), 153-161 Former BULLETIN OF SOCIETY …

The total domination number γ t (G) of a graph G is the minimum cardinality of a set S of
vertices so that every vertex of G is adjacent to a vertex in S. Our main result of this paper is …

A set S of vertices in a graph G is a dominating set of G if every vertex not in S is adjacent to
some vertex in S. The domination number, γ (G) γ (G), of G is the minimum cardinality of a …

Abstract Let G=(V, E) be a simple, nontrivial, finite, connected and undirected graph. For an
integer 1≤ k≤ diam (G), a distance k-dominating set of a connected graph G is a set S of …

We prove sharp bounds concerning domination number, radius, order and minimum degree
of a graph. In particular, we prove that if G is a connected graph of order n, domination …

Let be a non-complete connected graph of order greater or equal to 3 with vertex set and
edge set. An interior dominating set of is called a connected interior dominating set of if the …

The article's primary purpose is to develop methods for determining critical nodes, arcs, and
routes of transport and logistics networks. One of the proposed algorithms resolves a …

A vertex set S of a graph G is a dominating set if each vertex of G either belongs to S or is
adjacent to a vertex in S. The domination number γ (G) of G is the minimum cardinality of S …

A dominating set of a graph G=(V, E) is a subset of vertices S⊆ V such that every vertex v∈
V∖ S has at least one neighbor in S. Finding a dominating set with the minimum cardinality …