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On Signed Star domination in Graphs

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Acta Mathematicae Applicatae Sinica 2019年第2期35卷 452-457页

作者： Yan-cai ZHAO Er-fang SHAN Lian-ying MIAO Zuo-song LIANG Department of Basic Science Wuxi City College of Vocational Technology School of Management Shanghai University School of Mathematics China University of Mining and Technology School of Management Qufu Normal University

For a graph G =(V, E) without isolated vertex, a function f : E(G)→ {-1, 1}is said to be a signed star dominating function of G if■ f(e)≥1 for every v∈V(G), where E(v) ={uv∈E(G)|u∈V(G)}.The minimum value of ■f(e), taken over all signed star dominating functions f of G, is called the signed star domination number of G and is denoted by γss(G). This paper studies the bounds and algorithms of signed star domination numbers in some classes of graphs. In particular, sharp bounds for the signed star domination number of a general graph and a linear-time algorithm for the signed star domination problem in a tree is presented.

关键词： signed star domination bound graph algorithm tree

New Discoveries of domination Between Traffic Matrices

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Acta Mathematicae Applicatae Sinica 2017年第3期33卷 561-566页

作者： Peng-fei LIU Wen-guo YANG Tian-de GUO School of Mathematics Sciences University of Chinese Academy of SciencesBeijing 100049China Key Laboratory of Big Data Mining and Knowledge Management Chinese Academy of SciencesBeijing 100049China

In this paper the definition of domination is generalized to the case that the elements of the traffic matrices may have negative values. It is proved that D3 dominates D3 ＋ λ（D2 - D1） for any λ ≥0 if D1 dominates D2. Let u（D） be the set of all the traffic matrices that are dominated by the traffic matrix D. It is shown that u （ D∞） and u （D ∈） are isomorphic. Besides, similar results are obtained on multi-commodity flow problems. Fhrthermore, the results are the generalized to integral flows.

关键词： robust network design multi-commodity flows domination

The Product of the Restrained domination Numbers of a Graph and Its Complement

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Acta Mathematica Sinica,English Series 2014年第3期30卷 445-452页

作者： Johannes H.HATTINGH Ernst J.JOUBERT Department of Mathematics East Carolina University Department of Mathematics University of Johannesburg

Let G=（V,E） be a graph.A set S■V is a restrained dominating set if every vertex in V-S is adjacent to a vertex in S and to a vertex in V-S.The restrained domination number of G,denoted γr（G）,is the smallest cardinality of a restrained dominating set of G.In this paper,we show that if G is a graph of order n≥4,then γr（G）γr（G）≤2n.We also characterize the graphs achieving the upper bound.

关键词： Graph domination restrained domination Nordhaus-Gaddum upper bound

A lower bound on the total signed domination numbers of graphs

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Science China Mathematics 2007年第8期50卷 1157-1162页

作者： Xin-zhong LU Department of Mathematics,Zhejiang Normal University,Jinhua 321004,China Department of Mathematics Zhejiang Normal University Jinhua China

Let G be a finite connected simple graph with a vertex set V（G）and an edge set E（G）. A total signed domination function of G is a function f:V（G）∪E（G）→{-1,1}.The weight of f is W（f）=∑x∈V（G）∪E（G）)f（X）.For an element x∈V（G）∪E（G）,we define f[x]=∑y∈NT[x]f（y）.A total signed domination function of G is a function f:V（G）∪E（G）→{-1,1} such that f[x]≥1 for all x∈V（G）∪E（G）.The total signed domination numberγs*（G）of G is the minimum weight of a total signed domination function on G. In this paper,we obtain some lower bounds for the total signed domination number of a graph G and compute the exact values ofγs*（G）when G is Cn and Pn.

关键词： total signed domination function total signed domination number

The Sweatshop Workers of Nicaragua： Subjectivity, Labor, and domination

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Fudan Journal of the Humanities and Social Sciences 2017年第4期10卷 509-522页

作者： Natacha Borgeaud-Garciandfa CONICET/FLACSO Buenos Aires Argentina

This essay is based on an approach that addresses the relationship between work-related domination and the subjects who are submitted to it. This reflection arises from research undertaken in Nicaragua, among workers from the international textile factories known as maquiladoras (or maquilas). Men, but mostly young women, work and live here under particularly difficult conditions. The constraints of work and domination invade the recesses of their existence, and their power is such that it seems to annul any proper subjectivity. Although it may seem easy to locate the effects of work-related domination in the very intimacy of the subjects’ lives, it also appears as if part of themselves remains unsubdued. Dominated subjectivities can only rebel for failing to do it would be to condemn their beings to inexistence. What sense can be given to this gap in domination? Does it preserve the domination by preserving the subjects from the invasion in their own beings by this very domination? Is it only a resource of the submission? Those are, between domination and subjectivity, some of the aroused interrogations.

关键词： Labor domination Subjectivity Sweatshop workers Nicaragua

domination and Eternal domination of Jahangir Graph

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Open Journal of Discrete Mathematics 2019年第3期9卷 68-81页

作者： Ramy Shaheen Mohammad Assaad Ali Kassem Department of Mathematics Faculty of Science Tishreen University Lattakia Syria

In the eternal dominating set problem, guards form a dominating set on a graph and at each step, a vertex is attacked. We consider the “all guards move” of the eternal dominating set problem. In which one guard has to move to the attacked vertex and all the remaining guards are allowed to move to an adjacent vertex or stay in their current position after each attack. If the new formed set of guards is still a dominating set of the graph then we successfully defended the attack. Our goal is to find the minimum number of guards required to eternally protect the graph. We call this number the m-eternal domination number and we denote it by . In this paper we find the eternal domination number of Jahangir graph Js,m for s=2,3 and arbitrary m. We also find the domination number for J3,m .

关键词： Jahangir Graph Graph Protection domination Number Eternal domination

domination in Controlled and Observed Distributed Parameter Systems

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Intelligent Control and Automation 2013年第2期4卷 217-226页

作者： L. Afifi M. Joundi E. M. Magri A. El Jai Department of Mathematics and Computer Science Faculty of Sciences Ain Chock University of Hassan II Casablanca Casablanca Morocco MEPS-Systems Theory University of Perpignan Perpignan France

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.

关键词： Distributed Systems domination Actuators Sensors Compensation

domination Number of Square of Cartesian Products of Cycles

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Open Journal of Discrete Mathematics 2015年第4期5卷 88-94页

作者： Morteza Alishahi Sakineh Hoseini Shalmaee Islamic Azad University Nazarabad Branch

A set ?is a dominating set of G if every vertex of ?is adjacent to at least one vertex of S. The cardinality of the smallest dominating set of G is called the domination number of G. The square G2 of a graph G is obtained from G by adding new edges between every two vertices having distance 2 in G. In this paper we study the domination number of square of graphs, find a bound for domination number of square of Cartesian product of cycles, and find the exact value for some of them.

关键词： domination Number Square of a Graph Cartesian Product

A Graph Theory Based Self-Learning Honeypot to Detect Persistent Threats

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Intelligent Automation & Soft Computing 2023年第3期35卷 3331-3348页

作者： R.T.Pavendan K.Sankar K.A.Varun Kumar Department of Mathematics College of EngineeringAnna UniversityChennai600025India Department of Networking and Communications School of ComputingSRM Institute of Science and TechnologyKattankulathur602203India

Attacks on the cyber space is getting exponential in recent times.Illegal penetrations and breaches are real threats to the individuals and organizations.Conventional security systems are good enough to detect the known threats but when it comes to Advanced Persistent Threats(APTs)they fails.These APTs are targeted,more sophisticated and very persistent and incorporates lot of evasive techniques to bypass the existing defenses.Hence,there is a need for an effective defense system that can achieve a complete reliance of security.To address the above-mentioned issues,this paper proposes a novel honeypot system that tracks the anonymous behavior of the APT threats.The key idea of honeypot leverages the concepts of graph theory to detect such targeted attacks.The proposed honey-pot is self-realizing,strategic assisted which withholds the APTs actionable tech-niques and observes the behavior for analysis and modelling.The proposed graph theory based self learning honeypot using the resultsγ(C(n,1)),γc(C(n,1)),γsc(C(n,1))outperforms traditional techniques by detecting APTs behavioral with detection rate of 96%.

关键词： Graph theory domination Connected domination Secure Connected domination honeypot self learning ransomware