A note on the independent domination number in graphs
نویسندگان
چکیده
منابع مشابه
Independent domination in directed graphs
In this paper we initialize the study of independent domination in directed graphs. We show that an independent dominating set of an orientation of a graph is also an independent dominating set of the underlying graph, but that the converse is not true in general. We then prove existence and uniqueness theorems for several classes of digraphs including orientations of complete graphs, paths, tr...
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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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Let G be a simple graph of order n, maximum degree ∆ and minimum degree δ ≥ 2. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. The girth g(G) is the minimum length of a cycle in G. We establish sharp upper and lower bounds, as functions of n, ∆ and δ, for the independent domination number of graphs G with g(G) ...
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Let G be a simple graph of order n, maximum degree Δ and minimum degree δ ≥ 2. The independent domination number i(G) is defined to be the minimum cardinality among all maximal independent sets of vertices of G. The girth g(G) is the minimum length of a cycle in G. We establish best possible upper and lower bounds, as functions of n, Δ and δ, for the independent domination number of graphs G wi...
متن کاملOn the ratio of the domination number and the independent domination number in graphs
We let γ(G) and i(G) denote the domination number and the independent domination number ofG, respectively. Recently, Rad and Volkmann conjectured that i(G)/γ(G) ≤ ∆(G)/2 for every graph G, where ∆(G) is the maximum degree of G. In this note, we construct counterexamples of the conjecture for ∆(G) ≥ 6, and give a sharp upper bound of the ratio i(G)/γ(G) by using the maximum degree of G.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2013
ISSN: 0166-218X
DOI: 10.1016/j.dam.2013.07.009