A vertex of a graph is said to dominate itself and all of its neighbors. A double dominating set of a graph G is a set D of vertices of G such that every vertex of G is dominated by at least two vertices of D. The double domination number of a graph G is the minimum cardinality of a double dominating set of G. For a graph G = (V,E), a subset D ⊆ V (G) is a 2dominating set if every vertex of V (...

Let G be a graph. A set S of vertices in G dominates the graph if every vertex of G is either in S or a neighbor of a vertex in S. Finding a minimal cardinality set which dominates the graph is an NP-complete problem. The graph G is well-dominated if all its minimal dominating sets are of the same cardinality. The complexity status of recognizing well-dominated graphs is not known. We show that...

Top-k dominating queries combine the advantages of top-k queries and skyline queries, and eliminate their disadvantages. They return k objects with the highest domination score, which is defined as the number of dominated objects. As a top-k query, the user can bound the number of returned results through the parameter k, and like a skyline query a user-selected scoring function is not required...

An edge e ∈ E(G) dominates a vertex v ∈ V (G) if e is incident with v or e is incident with a vertex adjacent to v. An edge-vertex dominating set of a graph G is a set D of edges of G such that every vertex of G is edgevertex dominated by an edge of D. The edge-vertex domination number of a graph G is the minimum cardinality of an edge-vertex dominating set of G. A subset D ⊆ V (G) is a total d...

Dominance-based Rough Sets Approach (DRSA) is a generalized model of the classical Rough Sets Theory (RST) which may handle information with preference-ordered attribute domain. The attribute set in the information system may evolve over time. Approximations of DRSA used to induce decision rules need updating for knowledge discovery and other related tasks. We firstly introduce a kind of domina...

A node in a graph G = (V,E) is said to dominate itself and all nodes adjacent to it. A set S C V is a dominating set for G if each node in V is dominated by some node in S and is a double dominating set for G if each node in V is dominated by at least two nodes in S. First we give a brief survey of Nordhaus-Gaddum results for several domination-related parameters. Then we present new inequaliti...

A Mobile Ad Hoc Network (MANET) is an infrastructureless wireless network that can support highly dynamic mobile units. The multi-hop feature of a MANET suggests the use of clustering to simplify routing. Graph domination can be used in defining clusters in MANETs. A variant of dominating set which is more suitable for clustering MANETs is the weakly-connected dominating set. A cluster is defin...

A dominating set S of a graph G is called efficient if |N [v]∩S| = 1 for every vertex v ∈ V (G). That is, a dominating set S is efficient if and only if every vertex is dominated exactly once. In this paper, we investigate efficient multiple domination. There are several types of multiple domination defined in the literature: k-tuple domination, {k}-domination, and k-domination. We investigate ...