An Upper Bound for the Independent Domination Number
نویسندگان
چکیده
منابع مشابه
On trees attaining an upper bound on the total domination number
A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. The total domination number of a graph $G$, denoted by $gamma_t(G)$, is~the minimum cardinality of a total dominating set of $G$. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004), 6...
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A total outer-independent dominating set of a graph G = (V (G), E(G)) is a set D of vertices of G such that every vertex of G has a neighbor in D, and the set V (G) \D is independent. The total outer-independent domination number of a graph G, denoted by γ t (G), is the minimum cardinality of a total outer-independent dominating set of G. We prove that for every tree T of order n ≥ 4, with l le...
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A graph G is 2-stratified if its vertex set is colored into two nonempty classes, where one class of vertices colored red and the other color class blue. Let F be a 2-stratified graph rooted at one fixed blue vertex v. The F -domination number of G is the minimum number of red vertices of G in a red-blue coloring of the vertices of G such that for every blue vertex v of G, there is a copy of F ...
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In this paper, we provide an upper bound for the k-tuple domination number that generalises known upper bounds for the double and triple domination numbers. We prove that for any graph G, ×k(G) ln( − k + 2)+ ln(∑k−1 m=1(k −m)d̂m + )+ 1 − k + 2 n, where ×k(G) is the k-tuple domination number; is the minimal degree; d̂m is the m-degree of G; = 1 if k = 1 or 2 and =−d if k 3; d is the average degree...
متن کاملon trees attaining an upper bound on the total domination number
a total dominating set of a graph $g$ is a set $d$ of vertices of $g$ such that every vertex of $g$ has a neighbor in $d$. the total domination number of a graph $g$, denoted by $gamma_t(g)$, is~the minimum cardinality of a total dominating set of $g$. chellali and haynes [total and paired-domination numbers of a tree, akce international ournal of graphs and combinatorics 1 (2004), 6...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1999
ISSN: 0095-8956
DOI: 10.1006/jctb.1999.1907