A set S of vertices of a connected graph G=(V, E) is a connected dominating set of G if every
vertex of V− S is adjacent to at least one vertex of S and the subgraph induced by S is …

A set D of vertices in a graph G is a dominating set if every vertex in V (G)− D is adjacent to a
vertex in D. If the subgraph induced by the set D is connected, then D is a connected …

A Roman dominating function on a graph G=(V, E) is defined to be a function f: V→{0, 1, 2}
satisfying the condition that every vertex u for which f (u)= 0 is adjacent to at least one vertex …

The minimum weakly connected dominating set problem (MWCDSP), a variant of the
classical minimum dominating set problem, has extensive real-world applications, such as …

Abstract Let G=(V (G), E (G)) be a connected undirected graph. The closed neighborhood of
any vertex v∈ V (G) is NG [v]={u∈ V (G): uv∈ E (G)}∪{v}. For C⊆ V (G), the closed …

In this article, we focus on dominating set problems in graphs. We review the literature that
analyzes domination from different aspects, including bounds for the domination number …

A graph G is said to be k-γ c-critical if the connected domination number γ c (G) is equal to k
and γ c (G+ uv)< k for any pair of non-adjacent vertices u and v of G. Let ζ be the number of …

ABSTRACT A subset D of vertices in a graph G is an independent dominating set if D is a
dominating set and an independent set. A graph is independent domination edge …

A graph G for which γ R (G)= 2 γ (G) is the Roman graph, and if γ R wc (G)= 2 γ wc (G), then
G is the weakly connected Roman graph. In this paper, we show that the decision problem of …

Weakly Connected Independent and Weakly Connected Total Domination in a Product of
Graphs Page 1 Applied Mathematical Sciences, Vol. 8, 2014, no. 115, 5743 - 5749 HIKARI …