Total Bondage Number of a Graph
نویسنده
چکیده
A set D of a vertices in a graph G = (V,E) is said to be a total dominating set of G if every vertex in V is adjacent to some vertex in D. The total domination number γt(G) is the minimum cardinality of a total dominating set. If γt(G) = |V (G)| , the minimum cardinality of a set E0 ⊆ E(G), such that G−E0 contains no isolated vertices and γt(G− E0) > γt(G), is called the total bondage number of G. In this paper, we improve the earlier known upper bounds for the total bondage number of a graph.
منابع مشابه
On the complexity of some bondage problems in graphs
The paired bondage number (total restrained bondage number, independent bondage number, k-rainbow bondage number) of a graph G, is the minimum number of edges whose removal from G results in a graph with larger paired domination number (respectively, total restrained domination number, independent domination number, k-rainbow domination number). In this paper we show that the decision problems ...
متن کاملTotal Restrained Bondage in Graphs
A subset S of vertices of a graph G with no isolated vertex is a total restrained dominating set if every vertex is adjacent to a vertex in S and every vertex in V (G) − S is also adjacent to a vertex in V (G) − S. The total restrained domination number of G is the minimum cardinality of a total restrained dominating set of G. In this paper we initiate the study of total restrained bondage in g...
متن کاملComplexity of Bondage and Reinforcement
Let G = (V,E) be a graph. A subset D ⊆ V is a dominating set if every vertex not in D is adjacent to a vertex in D. A dominating set D is called a total dominating set if every vertex in D is adjacent to a vertex in D. The domination (resp. total domination) number of G is the smallest cardinality of a dominating (resp. total dominating) set of G. The bondage (resp. total bondage) number of a n...
متن کاملOn the complexity of the bondage and reinforcement problems
Let G = (V , E) be a graph. A subset D ⊆ V is a dominating set if every vertex not in D is adjacent to a vertex in D. A dominating set D is called a total dominating set if every vertex in D is adjacent to a vertex in D. The domination (resp. total domination) number of G is the smallest cardinality of a dominating (resp. total dominating) set of G. The bondage (resp. total bondage) number of a...
متن کاملUpper Bounds for Domination Related Parameters in Graphs on Surfaces
Abstract. In this paper we give tight upper bounds on the total domination number, the weakly connected domination number and the connected domination number of a graph in terms of order and Euler characteristic. We also present upper bounds for the restrained bondage number, the total restrained bondage number and the restricted edge connectivity of graphs in terms of the orientable/nonorienta...
متن کامل