total dominating set (or strongly-dominating set) is a set of vertices such that all vertices in the graph, including the vertices in the dominating set themselves...

all connected dominating sets of G. The connected domination number of G is the number of vertices in the minimum connected dominating set. Any spanning...

the set is known as a dominating set. Thus the Smith set is also called the smallest dominating set. The Schwartz set is equivalent to the Smith set, except...

mathematics In graph theory, an eternal dominating set for a graph G = (V, E) is a subset D of V such that D is a dominating set on which mobile guards are initially...

selecting a set of vertices (the dominating set) in a graph such that all other vertices are adjacent to at least one vertex in the dominating set. The Dominating...

set {a, c}. In this same graph, the maximal cliques are the sets {a, b} and {b, c}. A MIS is also a dominating set in the graph, and every dominating...

dominating set for a graph G = (V, E) is a subset D ⊆ E such that every edge not in D is adjacent to at least one edge in D. An edge dominating set is...

solution, the problem is W[2]-hard (due to a folklore reduction from the Dominating Set problem). Steiner Tree is also known to be APX-hard. However, there...

number: GT3  Dominating set, a.k.a. domination number: GT2  NP-complete special cases include the edge dominating set problem, i.e., the dominating set problem...

matching with k edges is an edge dominating set with k edges. Conversely, if we are given a minimum edge dominating set with k edges, we can construct a...

chessboard. Dominating sets represent arrangements of queens where every square is attacked or occupied by a queen; five queens, but no fewer, can dominate the...

finding the smallest index i such that Gi has a dominating set of size at most k. Although Dominating Set is NP-complete, the k-center problem remains NP-hard...

convergence theorem, application of function domination in measure theory Dominating set, in graph theory Domination (angel), in Christian angelology The Domination...

(1) a maximal independent set is a dominating set, and (2) the complement of a maximal independent set is also a dominating set if there are no isolated...

and states that, if γ(G) denotes the minimum number of vertices in a dominating set for the graph G, then γ ( G ◻ H ) ≥ γ ( G ) γ ( H ) . {\displaystyle...

vertices of the graph. It may also be called a dominating vertex, as it forms a one-element dominating set in the graph. A graph that contains a universal...

dominating sets. The domatic number of the graph is the maximum number of dominating sets in such a partition. dominating A dominating set is a set of...

bishops that can form an independent dominating set. By contrast, a total domination set, which is a dominating set for which every square, including those...

relations of this subject with square-blocking subsets and with perfect dominating sets (see below) in hypercubes were addressed by Dejter et al. since 1991...

graphs. These include the minimum dominating set, minimum connected dominating set, and minimum total dominating set problems. The chromatic number of...

funnel while the other would collect data from comparing the two sets of data. Dominator 2 features reinforced sheet metal and transparent Lexan has been...

another independent set is called maximal. Such sets are dominating sets. Every graph contains at most 3n/3 maximal independent sets, but many graphs have...

(\log n)}} under the exponential time hypothesis. Finding the smallest dominating set in a tournament. This is a subset of the vertices of the tournament...

Guha designed an approximation algorithms for the minimum connected dominating set problem that achieves a factor of 2 ln Δ + O(1), where Δ is the maximum...

and the universe entered a matter-dominated era. Recent results suggest that we have already entered an era dominated by dark energy, but examination of...

domatic partition: the set of the nodes with c(v) = 1 is a dominating set, and the set of the nodes with c(v) = 2 is another dominating set. Historically, weak...

non-dominating independence complex of G, denoted I'(G), is the abstract simplicial complex of the independent sets that are not dominating sets of G...

approximated within n + 1 in polynomial time. Min-ULR[>,≥] are minimum-dominating-set-hard, even with homogeneous systems and ternary coefficients (in {−1...

vertex cover. The complement of any maximal independent set must be a vertex cover. Min dominating set in bounded-degree graphs. The travelling salesman problem...

reaches a dominating set no larger than D {\displaystyle D} , so in particular when the starting set D {\displaystyle D} is a minimum dominating set this process...