Topic

# Domination analysis

About: Domination analysis is a(n) research topic. Over the lifetime, 3219 publication(s) have been published within this topic receiving 35833 citation(s).

##### Papers

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01 Jan 1998-

TL;DR: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms are presented.

Abstract: Bounds on the domination number domination, independence and irredundance efficiency, redundancy and the duals changing and unchanging domination conditions on the dominating set varieties of domination multiproperty and multiset parameters sums and products of parameters dominating functions frameworks for domination domination complexity and algorithms.

3,128 citations

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Brent N. Clark

^{1}, Brent N. Clark^{2}, Charles J. Colbourn^{1}, Charles J. Colbourn^{2}+2 more•Institutions (2)TL;DR: It is shown that many standard graph theoretic problems remain NP-complete on unit disks, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs.

Abstract: Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry. We show that many standard graph theoretic problems remain NP-complete on unit disk graphs, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs. In contrast, we give a polynomial time algorithm for finding cliques when the geometric representation (circles in the plane) is provided.

1,454 citations

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01 Jan 1998-

Abstract: LP-duality, complementarity and generality of graphical subset parameters dominating functions in graphs fractional domination and related parameters majority domination and its generalizations convexity of external domination-related functions of graphs combinatorial problems on chessboards - II domination in cartesian products - Vizing's conjecture algorithms complexity results domination parameters of a graph global domination distance domination in graphs domatic numbers of graphs and their variants - a survey domination-related parameters topics on domination in directed graphs graphs critical with respect to the domination number bondage, insensitivity and reinforcement.

1,260 citations

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TL;DR: Results concerning the total domination number of G (the smallest number of vertices in a total dominating set) and the total domatic number ofG (the largest order of a partition of G into total dominating sets) are obtained.

Abstract: A set D of vertices of a finite, undirected graph G = (V, E) is a total dominating set if every vertex of V is adjacent to some vertex of D. In this paper we initiate the study of total dominating sets in graphs and, in particular, obtain results concerning the total domination number of G (the smallest number of vertices in a total dominating set) and the total domatic number of G (the largest order of a partition of G into total dominating sets).

532 citations

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Ernest J. Cockayne

^{1}, Paul Dreyer^{2}, Sandra M. Hedetniemi^{3}, Stephen T. Hedetniemi^{3}•Institutions (3)TL;DR: The graph theoretic properties of this variant of the domination number of a graph G, a function f : V→{0,1,2} satisfying the condition that every vertex u is adjacent to at least one vertex v for which f(v)=2, are studied.

Abstract: A Roman dominating function on a graph G=(V,E) is a function f : V→{0,1,2} satisfying the condition that every vertex u for which f(u)=0 is adjacent to at least one vertex v for which f(v)=2. The weight of a Roman dominating function is the value f(V)=∑u∈Vf(u). The minimum weight of a Roman dominating function on a graph G is called the Roman domination number of G. In this paper, we study the graph theoretic properties of this variant of the domination number of a graph.

380 citations