Trees with Unique Minimum Dominating Sets
نویسندگان
چکیده
منابع مشابه
Trees with unique minimum total dominating sets
A set S of vertices of a graph G is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. We provide three equivalent conditions for a tree to have a unique minimum total dominating set and give a constructive characterization of such trees.
متن کاملTrees with unique minimum p - dominating sets ∗
Let p be a positive integer and G = (V,E) a simple graph. A p-dominating set of G is a subset S of V such that every vertex not in S is dominated by at least p vertices in S. The p-domination number γp(G) is the minimum cardinality among the p-dominating sets of G. In this paper, for p ≥ 2, we give three equivalent conditions for trees with unique minimum p-dominating sets and also give a const...
متن کاملBlock graphs with unique minimum dominating sets
For any graph G a set D of vertices of G is a dominating set, if every vertex v∈V (G)− D has at least one neighbor in D. The domination number (G) is the smallest number of vertices in any dominating set. In this paper, a characterization is given for block graphs having a unique minimum dominating set. With this result, we generalize a theorem of Gunther, Hartnell, Markus and Rall for trees. c...
متن کاملA Review on Graphs with Unique Minimum Dominating Sets
A dominating set for a graph G is a subset D of V such that every vertex not in D is adjacent to at least one member of D. This paper deals with some of the graphs having unique minimum dominating sets. We also find a unique minimum dominating sets for block graphs and maximum graphs.
متن کاملTrees with two disjoint minimum independent dominating sets
The independent domination number of a graph G, denoted i(G), is the minimum cardinality of a maximal independent set of G. A maximal independent set of cardinality i(G) in G we call an i(G)-set. In this paper we provide a constructive characterization of trees G that have two disjoint i(G)-sets. © 2005 Elsevier B.V. All rights reserved.
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ژورنال
عنوان ژورنال: International Journal of Soft Computing, Mathematics and Control
سال: 2015
ISSN: 2201-4160
DOI: 10.14810/ijscmc.2015.4102