منابع مشابه
Block 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 کاملTrees 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 کاملEfficient Dominating and Edge Dominating Sets for Graphs and Hypergraphs
Let G = (V,E) be a graph. A vertex dominates itself and all its neighbors, i.e., every vertex v ∈ V dominates its closed neighborhood N [v]. A vertex set D in G is an efficient dominating (e.d.) set for G if for every vertex v ∈ V , there is exactly one d ∈ D dominating v. An edge set M ⊆ E is an efficient edge dominating (e.e.d.) set for G if it is an efficient dominating set in the line graph...
متن کاملEfficient dominating sets in Cayley graphs
An independent set C of vertices in a graph is an efficient dominating set (or perfect code) when each vertex not in C is adjacent to exactly one vertex in C. An E-chain is a countable family of nested graphs, each of which has an efficient dominating set. The Hamming codes in the n-cubes provide a classical example of E-chains. We give a constructing tool to produce E-chains of Cayley graphs. ...
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ژورنال
عنوان ژورنال: Open Journal of Discrete Mathematics
سال: 2020
ISSN: 2161-7635,2161-7643
DOI: 10.4236/ojdm.2020.102006