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Integrated dominating and hit set-inspired unequal clusteringbased data aggregation in wireless sensor networks

International Journal of Intelligent Computing and Cybernetics 2022年第4期15卷 642-655页

作者： G.Vennira Selvi V.Muthukumaran A.C.Kaladevi S.Satheesh Kumar B.Swapna Department of Computer Science and Engineering Global Institute of Engineering and TechnologyVelloreIndia Department of Mathematics School of Applied SciencesREVA UniversityBangaloreIndia Department of Computer Science and Engineering Sona College of TechnologySalemIndia Department of Computer Science School of Applied SciencesREVA UniversityBangaloreIndia Department of Electronics and Communication Engineering Dr MGR Educational and Research InstituteChennaiIndia

Purpose-In wireless sensor networks,improving the network lifetime is considered as the prime objective that needs to be significantly addressed during data *** the traditional data aggregation techniques,cluster-based dominating set algorithms are identified as more effective in aggregating data through cluster ***,the existing cluster-based dominating set algorithms suffer from a major drawback of energy deficiency when a large number of communicating nodes need to collaborate for transferring the aggregated ***,due to this reason,the energy of each communicating node is gradually decreased and the network lifetime is also *** increase the lifetime of the network,the proposed algorithm uses two sets:dominating set and hit ***/methodology/approach-The proposed algorithm uses two sets:dominating set and hit *** dominating set constructs an unequal clustering,and the hit set minimizes the number of communicating nodes by selecting the optimized cluster head for transferring the aggregated data to the base *** simulation results also infer that the proposed optimized unequal clustering algorithm(OUCA)is greater in improving the network lifetime to a maximum amount of 22%than the existing cluster head selection approach considered for ***-In this paper,lifetime of the network is prolonged by constructing an unequal cluster using the dominating set and electing an optimized cluster head using hit *** dominator set chooses the dominator based on the remaining energy and its node degree of each *** optimized cluster head is chosen by the hit set to minimize the number of communicating nodes in the *** proposed algorithm effectively constructs the clusters with a minimum number of communicating nodes using the dominating and hit *** simulation result confirms that the proposed algorithm prolonging the lifetime of the network efficiently when compared with the existing algorithms.

关键词： Unequal clustering Hit set dominating set Network lifetime

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有向路和有向圈的控制集数

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高等学校计算数学学报 2007年第1期29卷 74-79页

作者：罗永萍杨爱民山西大学数学科学学院山西大学数学科学学院太原 030006

1引言设G=（V,E）为无向图．子集D （?）V（G）是无向图G的控制集,如果对于任意的y,∈V（G）-D,都存在x∈D,使xy∈E（G）．G的控制集D是G的分裂控制集,如果G中由V（G）-D导出的子图G〈V（G）-D〉是不连通的．G的一个控制集D是G的一个强... 详细信息

1引言设G=（V,E）为无向图．子集D （?）V（G）是无向图G的控制集,如果对于任意的y,∈V（G）-D,都存在x∈D,使xy∈E（G）．G的控制集D是G的分裂控制集,如果G中由V（G）-D导出的子图G〈V（G）-D〉是不连通的．G的一个控制集D是G的一个强（弱）控制集,若dG（x）≥d;（y）(d;（x）≤d;（y）),其中d;（x）表示G中与点x关联的边数．对于有向图H=（V,A）,子集D（?）V（H）称为H的控制集,如果对于任意的y∈

关键词： dominating set split dominating set strong(weak)dominating set

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Domination Number in Graphs with Minimum Degree Two

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Acta Mathematica Sinica,English Series 2009年第8期25卷 1253-1268页

作者： Er Fang SHAN Moo Young SOHN Xu Dong YUAN Michael A. HENNING Department of Mathematics Shanghai University Shanghai 200444 P. R. China Department of Applied Mathematics Changwon National University 641-773 Changwon Korea Department of Mathematics Guangxi Normal University Guilin 541004 P. R. China School of Mathematical Sciences University of KwaZulu-Natal Pietermaritzburg 3209 South Africa

A set D of vertices of a graph G = （V, E） is called a dominating set if every vertex of V not in D is adjacent to a vertex of D. In 1996, Reed proved that every graph of order n with minimum degree at least 3 has a dominating set of cardinality at most 3n/8. In this paper we generalize Reed＇s result. We show that every graph G of order n with minimum degree at least 2 has a dominating set of cardinality at most （3n ＋IV21）/8, where V2 denotes the set of vertices of degree 2 in G. As an application of the above result, we show that for k ≥ 1, the k-restricted domination number rk （G, γ） ≤ （3n＋5k）/8 for all graphs of order n with minimum degree at least 3.

关键词： graph dominating set domination number restricted domination number

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Distance domination of generalized de Bruijn and Kautz digraphs

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Frontiers of Mathematics in China 2017年第2期12卷 339-357页

作者： Yanxia DONG Erfang SHAN Xiao MIN Department of Mathematics Shanghai University Shanghai 200444 China School of Management Shanghai University Shanghai 200444 China School of Statistics and Information Shanghai University of International Business and Economics Shanghai 201620 China College of Mathematics Physics and Information Engineering Jiaxing University Jiaxing 314001 China

Let G= （V,A） be adigraph and k ≥ 1 an integer. For u,v ∈ V, we say that the vertex u distance k-dominate v if the distance from u to v at most k. A set D of vertices in G is a distance k-dominating set if each vertex of V ／ D is distance k-dominated by some vertex of D. The distance k-domination number of G, denoted by γk（G）, is the minimum cardinality of a distance k-dominating set of G. Generalized de Bruijn digraphs GB（n, d） and generalized Kautz digraphs Gg（n, d） are good candidates for interconnection k networks. Denote △k ：=（∑j^k=0 d^j）^-1. F. Tian and J. Xu showed that [n△k] ≤ γk（GB（n,d）） ≤ [n/d^k] and [n△k] ≤ γk（GK（n,d）） ≤ [n/d^k]. In this paper, we prove that every generalized de Bruijn digraph GB（n, d） has the distance k- domination number [n△k] or [n△k] ＋ 1, and the distance k-domination number of every generalized Kautz digraph GK（n, d） bounded above by [n/ （d^k-1 ＋d^k）]. Additionally, we present various sufficient conditions for γk（GB（n, d）） = [n△k] and γk（GK（n, d）） = [n△k].

关键词： Combinatorial problems dominating set distance dominating set,generalized de Bruijn digraph generalized Kautz digraph

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Bondage number of mesh networks

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Frontiers of Mathematics in China 2012年第5期7卷 813-826页

作者： Futao HU Jun-Ming XU School of Mathematical Sciences University of Science and Technology of China Wentsun Wu Key Laboratory of Chinese Academy of Sciences Hefei 230026 China

The bondage number b（G） of number of edges whose removal from G number greater than that of G. Denote a nonempty graph G is the smallest results in a graph with domination Pn × Pm the Cartesian product of two paths Pn and Pm. This paper determines the exact values of b（Pn × P2）, b（Pn × P3）, and b（Pn × P4） for n ≥ 2.

关键词： Bondage number dominating set domination number mesh network

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The Limit Case of a Domination Property

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Acta Mathematica Sinica,English Series 2012年第3期28卷 463-468页

作者： Magdalena LEMANSKA Juan A. RODRíGUEZ-VELZQUEZ Ismael G. YERO Department of Technical Physics and Applied Mathematics Gdańsk University of Technology Departament d’Enginyeria Informàtica i Matemàtiques Universitat Rovira i Virgili Departament d'Enginyeria Informàtica i Matemàtiques Universitat Rovira i Virgili

The domination number γ,（G） of a connected graph G of order n is bounded below by

关键词： dominating set domination number

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An energy-degree evaluation metric for clustering purposes in mobile ad hoc networks

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International Journal of Modeling, Simulation, and Scientific Computing 2019年第2期10卷 114-132页

作者： Khalil Amine MOAD6 Research Team MASI LaboratoryE3S Research Centre Mohammadia School of Engineering Mohammed V University of RabatMorocco

Network clustering is the process of partitioning a network into a number of virtual entities mastered by certain nodes,called cluster centers that are responsible for collecting and maintaining topology information and managing the routing *** ad hoc networking,clustering has been introduced to deal with the dynamic topology by providing a temporarily stable network *** process mainly depends on the metric upon which the selection of cluster centers is performed.A wide range of clustering metrics were introduced in the literature based on network issues including mobility and connectivity degree,giving rise to a variety of clustering *** clustering provides energy consumption reduction,residual energy has not received enough attention and few studies have addressed the clustering on the basis of this *** paper discusses the current clustering metrics and proposes an energy-degree evaluation metric with mobility consideration taking into account the nodes residual energy and the network connectivity as two main keys of clustering.

关键词： Ad hoc networks clustering dominating set energy aware mobility

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SOME RESULTS ON DOMINATION NUMBER OF PRODUCTS OF GRAPHS

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Applied Mathematics(A Journal of Chinese Universities) 1998年第1期13卷 103-108页

作者： SHANERFANG SUNLIANG KANGLIYING DepartmentofMathematics ShijiazhuangNormalCollegeShijdazhuang050041. DepartmentofAppliedMathematics BeijingInstituteofTechnologyBeijing100081. DepartmentofBasicCourses ShijiazhuangRailwayInstituteShijiazhueng050043.

Let G=(V,E) be a simple graph. A subset D of V is called a dominating set of G if for every vertex x∈V-D,x is adjacent to at least one vertex of D . Let γ(G) and γ c(G) denote the ... 详细信息

Let G=(V,E) be a simple graph. A subset D of V is called a dominating set of G if for every vertex x∈V-D,x is adjacent to at least one vertex of D . Let γ(G) and γ c(G) denote the domination and connected domination number of G , respectively. In 1965,Vizing conjectured that if G×H is the Cartesian product of G and H , thenγ(G×H)≥γ(G)·γ(H).In this paper, it is showed that the conjecture holds if γ(H) ≠ γ c(H) .And for paths P m and P n , a lower bound and an upper bound for γ(P m×P n) are obtained.

关键词： Graph dominating set products.

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Generating Storyline with Societal Risk from Tianya Club

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Journal of Systems Science and Information 2017年第6期8卷 524-536页

作者： Yugai JIA Xijin TANG Academy of Mathematics and Systems Science Chinese Academy of Sciences University of Chinese Academy of Sciences

Major societal problems affect the social stability. It is necessary to understand the public opinion toward those issues to avoid social conflicts. Nowadays the social media become the major platform to track what the public is concerned about and which may be of the societal risk. However,it is very tough to capture the public attention in short time due to huge flow of user-generated *** this paper, we approach this problem by expanding the method of generating storyline with the result displayed by a multi-view graph. One real-world example is illustrated and evaluation is given to show the effectiveness of the proposed method.

关键词： societal risk storyline multi-view graph dominating set χ~2 statistic

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IS γα≤δ FOR GRAPHS WHICH HAVE DIAMETER TWO?

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Journal of Systems Science & Complexity 2003年第2期16卷 195-198页

作者： CHENYaojun ZHANGYunqing ZHANGKemin DepartmentofMathematics NanjingUniversityNanjing210093China DepartmentofMathematics ShaanxiNormalUniversityXi'an710062China

A subset of S of the vertex set of a graph G is called acyclic if the subgraph it induces in G contains no cycles. S is called an acyclic dominating set of G if it is both acyclic and dominating. The minimum cardinality of an acyclic dominating set, denoted by γα(G), is called the acyclic domination number of G. S. M. Hedetniemi et al. on 2000 introduced the concept of acyclic domination and posed the following open problem: Is γα(G) ≤ δ(G) for any graph whose diameter is two? In this paper, we give a counterexample which disproves the problem.

关键词： dominating set acyclic diameter two

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