Irredundance number versus domination number
نویسندگان
چکیده
منابع مشابه
The ratio of the irredundance number and the domination number for block-cactus graphs
Let γ(G) and ir(G) denote the domination number and the irredundance number of a graph G, respectively. Allan and Laskar [1] and Bollobás and Cockayne [2] proved independently that γ(G) < 2 ir(G) for any graph G. For a tree T , Damaschke [4] obtained the sharper estimation 2γ(T ) < 3 ir(T ). Extending Damaschke’s result, Volkmann [11] proved that 2γ(G) ≤ 3 ir(G) for any block graph G and for an...
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A vertex v in a vertex-subset I of an undirected graph G is said to be redundant if its closed neighborhood is contained in the union of closed neighborhoods of vertices of I − {v}. In the context of a communication network , this means that any vertex that may receive communications from I may also be informed from I − {v} . The irredundance number ir(G) is the minimum cardinality taken over a...
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The open neighborhood of a vertex $v$ of a graph $G$ is the set $N(v)$ consisting of all vertices adjacent to $v$ in $G$. For $Dsubseteq V(G)$, we define $overline{D}=V(G)setminus D$. A set $Dsubseteq V(G)$ is called a super dominating set of $G$ if for every vertex $uin overline{D}$, there exists $vin D$ such that $N(v)cap overline{D}={u}$. The super domination number of $G$ is the minimum car...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1991
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90403-o