Total restrained domination numbers of trees
نویسندگان
چکیده
منابع مشابه
Trees with Equal Restrained Domination and Total Restrained Domination Numbers
For a graph G = (V,E), a set D ⊆ V (G) is a total restrained dominating set if it is a dominating set and both 〈D〉 and 〈V (G)−D〉 do not have isolated vertices. The cardinality of a minimum total restrained dominating set in G is the total restrained domination number. A set D ⊆ V (G) is a restrained dominating set if it is a dominating set and 〈V (G) − D〉 does not contain an isolated vertex. Th...
متن کاملTotal restrained domination numbers of trees
For a given connected graphG= (V ,E), a setDtr ⊆ V (G) is a total restrained dominating set if it is dominating and both 〈Dtr〉 and 〈V (G)−Dtr〉 do not contain isolate vertices. The cardinality of the minimum total restrained dominating set in G is the total restrained domination number and is denoted by tr(G). In this paper we characterize the trees with equal total and total restrained dominati...
متن کاملTrees with Equal Total Domination and Total Restrained Domination Numbers
For a graph G = (V, E), a set S ⊆ V (G) is a total dominating set if it is dominating and both 〈S〉 has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number. A set S ⊆ V (G) is a total restrained dominating set if it is total dominating and 〈V (G) − S〉 has no isolated vertices. The cardinality of a minimum total restrained dominating set in ...
متن کاملTotal restrained domination in trees
Let G = (V,E) be a graph. A set S ⊆ V is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex of V − S is adjacent to a vertex in V − S. The total restrained domination number of G, denoted by γtr(G), is the smallest cardinality of a total restrained dominating set of G. We show that if T is a tree of order n, then γtr(T ) ≥ d(n + 2)/2e. Moreover, we s...
متن کاملTrees with Equal Domination and Restrained Domination Numbers
Let G = (V, E) be a graph and let S ⊆ V . The set S is a packing in G if the vertices of S are pairwise at distance at least three apart in G. The set S is a dominating set (DS) if every vertex in V − S is adjacent to a vertex in S. Further, if every vertex in V − S is also adjacent to a vertex in V − S, then S is a restrained dominating set (RDS). The domination number of G, denoted by γ(G), i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.03.041