20 pages, 12 figuresA set $S\subseteq V(G)$ of a graph $G$ is a dominating set if each vertex has a neighbor in $S$ or belongs to $S$. Let $\gamma(G)$ be the cardinality of a minimum dominating set in $G$. The bondage number $b(G)$ of a graph $G$ is the smallest number of edges $A\subseteq E(G)$, such that $\gamma(G-A)=\gamma(G)+1$. The problem of finding $b(G)$ for a graph $G$ is known to be NP-hard even for bipartite graphs. In this paper, we show that deciding if $b(G)=1$ is NP-hard, while deciding if $b(G)=2$ is coNP-hard, even when $G$ is restricted to one of the following classes: planar $3$-regular graphs, planar claw-free graphs with maximum degree $3$, planar bipartite graphs of maximum degree $3$ with girth $k$, for any fixed $k\g...
AbstractThe bondage number b(G) of a nonempty graph G is defined to be the cardinality of the smalle...
<p>The bondage number b(G) of a graph G is the smallest number<br /> of edges whose removal from G r...
The DOMINATING SET problem is one of the most widely studied problems in graph theory and networking...
AbstractThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges ...
AbstractA set D of vertices in a graph G is a dominating set if each vertex of G that is not in D is...
A set $S\subseteq V(G)$ of a graph $G$ is a dominating set if each vertex has a neighbor in $S$ or b...
A set $S\subseteq V(G)$ of a graph $G$ is a dominating set if each vertex has a neighbor in $S$ or b...
AbstractLet G=(V,E) be a simple graph. A subset S of V is a dominating set of G if for any vertex v∈...
AbstractThe bondage number b(G) of a nonempty graph G is defined to be the cardinality of the smalle...
The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every...
AbstractLet G=(V,E) be a graph. A subset D⊆V is a dominating set if every vertex not in D is adjacen...
Abstract: Let G = (V, E) be a simple graph on the vertex set V . In a graph G, A set S ⊆ V is a domi...
AbstractThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest edge set whos...
AbstractThe domination number of a graph is the minimum number of vertices in a set S such that ever...
AbstractThe bondage number b(G) of a graph G is the minimum cardinality of a set of edges of G whose...
AbstractThe bondage number b(G) of a nonempty graph G is defined to be the cardinality of the smalle...
<p>The bondage number b(G) of a graph G is the smallest number<br /> of edges whose removal from G r...
The DOMINATING SET problem is one of the most widely studied problems in graph theory and networking...
AbstractThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges ...
AbstractA set D of vertices in a graph G is a dominating set if each vertex of G that is not in D is...
A set $S\subseteq V(G)$ of a graph $G$ is a dominating set if each vertex has a neighbor in $S$ or b...
A set $S\subseteq V(G)$ of a graph $G$ is a dominating set if each vertex has a neighbor in $S$ or b...
AbstractLet G=(V,E) be a simple graph. A subset S of V is a dominating set of G if for any vertex v∈...
AbstractThe bondage number b(G) of a nonempty graph G is defined to be the cardinality of the smalle...
The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every...
AbstractLet G=(V,E) be a graph. A subset D⊆V is a dominating set if every vertex not in D is adjacen...
Abstract: Let G = (V, E) be a simple graph on the vertex set V . In a graph G, A set S ⊆ V is a domi...
AbstractThe bondage number b(G) of a nonempty graph G is the cardinality of a smallest edge set whos...
AbstractThe domination number of a graph is the minimum number of vertices in a set S such that ever...
AbstractThe bondage number b(G) of a graph G is the minimum cardinality of a set of edges of G whose...
AbstractThe bondage number b(G) of a nonempty graph G is defined to be the cardinality of the smalle...
<p>The bondage number b(G) of a graph G is the smallest number<br /> of edges whose removal from G r...
The DOMINATING SET problem is one of the most widely studied problems in graph theory and networking...