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Search Results: 1 - 10 of 244 matches for " domination "
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Dominating Sets and Domination Polynomials of Square of Paths  [PDF]
A. Vijayan, K. Lal Gipson
Open Journal of Discrete Mathematics (OJDM) , 2013, DOI: 10.4236/ojdm.2013.31013
Abstract: Let G = (V, E) be a simple graph. A set S í V is a dominating set of G, if every vertex in V-S is adjacent to at least one vertex in S. Let \"\" be the square of the Path \"\" and let \"\" denote the family of all dominating sets of \"\" with cardinality i. Let\"\" . In this paper, we obtain a recursive formula for \"\". Using this recursive formula, we construct the polynomial,\"\" , which we call domination polynomial of \"\" and obtain some properties of this polynomial.
On the Injective Equitable Domination of Graphs  [PDF]
Ahmad N. Alkenani, Hanaa Alashwali, Najat Muthana
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.717169
Abstract: A dominating set D in a graph G is called an injective equitable dominating set (Inj-equitable dominating set) if for every \"\", there exists \"\"such that u is adjacent to v and \"\". The minimum cardinality of such a dominating set is denoted by \"\"and is called the Inj-equitable domination number of G. In this paper, we introduce the injective equitable domination of a graph and study its relation with other domination parameters. The minimal injective equitable dominating set, the injective equitable independence number \"\", and the injective equitable domatic number \"\"are defined.
A Lemma on Almost Regular Graphs and an Alternative Proof for Bounds on γt (Pk □ Pm)  [PDF]
Paul Feit
Open Journal of Discrete Mathematics (OJDM) , 2013, DOI: 10.4236/ojdm.2013.34031
Abstract:

Gravier et al. established bounds on the size of a minimal totally dominant subset for graphs PkPm. This paper offers an alternative calculation, based on the following lemma: Let \"\" so k≥3 and r≥2. Let H be an r-regular finite graph, and put G=PkH. 1) If a perfect totally dominant subset exists for G, then it is minimal; 2) If r>2 and a perfect totally dominant subset exists for G, then every minimal totally dominant subset of G must be perfect. Perfect dominant subsets exist for Pk Cn when k and n satisfy specific modular conditions. Bounds for rt(Pk

Bounds for Domination Parameters in Cayley Graphs on Dihedral Group  [PDF]
T. Tamizh Chelvam, G. Kalaimurugan
Open Journal of Discrete Mathematics (OJDM) , 2012, DOI: 10.4236/ojdm.2012.21002
Abstract: In this paper, sharp upper bounds for the domination number, total domination number and connected domination number for the Cayley graph G = Cay(D2n, Ω) constructed on the finite dihedral group D2n, and a specified generating set Ω of D2n. Further efficient dominating sets in G = Cay(D2n, Ω) are also obtained. More specifically, it is proved that some of the proper subgroups of D2n are efficient domination sets. Using this, an E-chain of Cayley graphs on the dihedral group is also constructed.
Vertices belonging to all or to no minimum locating dominating sets of trees
Mostafa Blidia,Rahma Lounes
Opuscula Mathematica , 2009,
Abstract: A set $D$ of vertices in a graph $G$ is a locating-dominating set if for every two vertices $u, v$ of $G \setminus D$ the sets $N(u) \cap D$ and $N(v) \cap D$ are non-empty and different. In this paper, we characterize vertices that are in all or in no minimum locating dominating sets in trees. The characterization guarantees that the $\gamma_L$-excellent tree can be recognized in a polynomial time.
Some New Results on Domination Integrity of Graphs  [PDF]
Samir K. Vaidya, Nirang J. Kothari
Open Journal of Discrete Mathematics (OJDM) , 2012, DOI: 10.4236/ojdm.2012.23018
Abstract: The domination integrity of a connected graph G= (V(G), E(G)) is denoted as DI(G) and defined by DI(G) = min{*S*+ m(G-S) : S is a dominating set } where m(G-S) is the order of a maximum component of G-S . We discuss domination integrity in the context of some graph operations like duplication of an edge by vertex and duplication of vertex by an edge.
Total Domination number of Generalized Petersen Graphs  [PDF]
Jianxiang CAO, Weiguo LIN, Minyong SHI
Intelligent Information Management (IIM) , 2009, DOI: 10.4236/iim.2009.11003
Abstract: Generalized Petersen graphs are an important class of commonly used interconnection networks and have been studied . The total domination number of generalized Petersen graphs P(m,2) is obtained in this paper.
Edge-Vertex Dominating Sets and Edge-Vertex Domination Polynomials of Cycles  [PDF]
A. Vijayan, J. Sherin Beula
Open Journal of Discrete Mathematics (OJDM) , 2015, DOI: 10.4236/ojdm.2015.54007
Abstract: Let G = (V, E) be a simple graph. A set S \"\"E(G) is an edge-vertex dominating set of G (or simply an ev-dominating set), if for all vertices v \"\"V(G); there exists an edge e\"\"S such that e dominates v. Let \"\" denote the family of all ev-dominating sets of \"\" with cardinality i. Let \"\". In this paper, we obtain a recursive formula for \"\". Using this recursive formula, we construct the polynomial,\"\" , which we call edge-vertex domination polynomial of \"\" (or simply an ev-domination polynomial of \"\") and obtain some properties of this polynomial.
DOUBLE DOMINATION NUMBER AND CONNECTIVITY OF GRAPHS
C. Sivagnanam
International Journal of Digital Information and Wireless Communications , 2012,
Abstract: In a graph G, a vertex dominates itself and its neighbours. A subset S of V is called a dominating set in G if every vertex in V is dominated by at least one vertex in S. The domination number is the minimum cardinality of a dominating set. A set is called a double dominating set of a graph G if every vertex in V is dominated by at least two vertices in S. The minimum cardinality of a double dominating set is called double domination number of G and is denoted by dd(G). The connectivity of a connected graph G is the minimum number of vertices whose removal results in a disconnected or trivial graph. In this paper we find an upper bound for the sum of the double domination number and connectivity of a graph and characterize the corresponding extremal graphs.
Domination in Controlled and Observed Distributed Parameter Systems  [PDF]
L. Afifi, M. Joundi, E. M. Magri, A. El Jai
Intelligent Control and Automation (ICA) , 2013, DOI: 10.4236/ica.2013.42026
Abstract: We consider and we study a general concept of domination for controlled and observed distributed systems. We give characterization results and the main properties of this notion for controlled systems, with respect to an output operator. We also examine the case of actuators and sensors. Various other situations are considered and applications are given. Then, we extend this study by comparing observed systems with respect to a control operator. Finally, we study the relationship between the notion of domination and the compensation one, in the exact and weak cases.
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