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A Lower Bound for the Algebraic Connectivity of a Graph in Terms of the domination number

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Acta Mathematicae Applicatae Sinica 2018年第4期34卷 752-760页

作者： Yi-Zheng FAN Ying-Ying TAN School of Mathematical Sciences Anhui University Hefei 230601 P. R. China School of Mathematics and Physics Anhui Jianzhu University Hefei 230601 China

We investigate how the algebraic connectivity of a graph changes by relocating a connected branch from one vertex to another vertex, and then minimize the algebraic connectivity among all connected graphs of order n with fixed domination number γ≤（n＋2）/3, and finally present a lower bound for the algebraic connectivity in terms of the domination number. We also characterize the minimum algebraic connectivity of graphs with domination number half their order.

关键词： graph algebraic connectivity domination number

On the Characterization of Maximal Planar Graphs with a Given Signed Cycle domination number

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Acta Mathematica Sinica,English Series 2018年第5期34卷 911-920页

作者： Xiao Ming PI Department of Mathematics Harbin Normal University

Let G = （V, E） be a simple graph. A function f ： E → {＋1,-1} is called a signed cycle domination function （SCDF） of G if ∑e∈E（C） f（e） ≥ 1 for every induced cycle C of G. The signed cycle domination number of G is defined as γ′sc（G） = min{∑e∈E f（e）｜ f is an SCDF of G}. This paper will characterize all maxima] planar graphs G with order n ≥ 6 and γ′sc（G） =n.

关键词： domination number signed cycle domination function signed cycle domination number planar graph maximal planar graph

Some Upper Bounds Related with domination number

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Journal of the Operations Research Society of China 2013年第2期1卷 217-225页

作者： Zhao Gu Jixiang Meng Zhao Zhang Jin E.Wan College of Mathematics and System Sciences Xin Jiang UniversityUrumqi 830046China College of Information Science and Engineering Xin Jiang UniversityUrumqi 830046China

For a simple and connected graph G,denote the domination number,the diameter,and the radius of G asβ(G),D(G),and r(G),*** this paper,we solve two conjectures on the upper bounds ofβ(G)·D(G)andβ(G)+r(G),which are p... 详细信息

关键词： AutoGraphiX Upper bounds Extremal tree domination number

Characterization of Connected Graphs with Maximum domination number

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Journal of Mathematical Research and Exposition 2000年第4期20卷 523-528页

作者：徐保根周尚超华东交通大学数学系南昌330013

Let G be a connected graph of order p, and let γ7(G) denote the domination number of G. Clearly, γ(G) ≤[p/2]. The aim of this paper is to characterize the graphs G that reaches this upper bound. The main results are as follows: (1) when p is even, γ(G) = p/2 if and only if either G C4 or G is the crown of a connected graph with p/2 vertices; (2) when p is odd, γ(G) = (p-1)/2 if and only if every spanning tree of G is one of the two classes of trees shown in Theorem 3.1.

关键词： connected graph crown domination number domination critical graph$

domination numbers of Undirected Toroidal Mesh

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Acta Mathematica Sinica,English Series 2012年第3期28卷 453-462页

作者： Xin XIE Jun Ming XU Department of Mathematics Huangshan University Department of Mathematics University of Science and Technology of China

The （d, m）-domination number γd,m is a new measure to characterize the reliability of resources-sharing in fault tolerant networks, in some sense, which can more accurately characterize the reliability of networks ... 详细信息

关键词： Undirected toroidal mesh reliability m-diameter domination number

Construction of an Energy-Efficient Detour Non-Split Dominating Set in WSN

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Computers, Materials & Continua 2022年第10期73卷 689-700页

作者： G.Sheeba T.M.Selvarajan Department of Mathematics Government Engineering CollegeTrivandrum695035India Department of Mathematics Noorul Islam Centre for Higher EducationKumaracoilThuckalay629175India

Wireless sensor networks(WSNs)are one of the most important improvements due to their remarkable capacities and their continuous growth in various ***,the lifetime of WSNs is very confined because of the delimited energy limit of their sensor *** is the reason why energy conservation is considered the main exploration worry for *** this energy-efficient routing is required to save energy and to subsequently drag out the lifetime of *** this report we use the Ant Colony Optimization(ACO)method and are evaluated using the Genetic Algorithm(GA),based on the Detour non-split dominant set(GA)In this research,we use the energy efficiency returnee non-split dominating set(DNSDS).A set S⊆V is supposed to be a DNSDS of G when the graph G=(V,E)is expressed as both detours as well as a non-split dominating set of *** the detour non-split domination number be addressed asγ_dns(G)and is the minimum order of its detour non-split dominating *** DNSDS of orderγdns(G)is aγdns-set of ***,theγ_dns(G)of various standard graphs is resolved and some of its general properties are contemplated.A connected graph usually has an order n with detour non-split domination number as n or n–1 are *** connected graphs of order n≥4 and detour diameter D≤4 with detour non-split dominating number n or n−1 or n−2 are additionally *** considering any pair of positive integers to be specific a and b,there exists a connected graph G which is normally indicated as dn(G)=a,γ(G)=b andγdns(G)=a+b−2,hereγdns(G)indicates the detour domination number and dn(G)indicates the detour number of a *** time is taken for the construction and the size of DNSDS are considered for examining the performance of the proposed *** simulation result confirms that the DNSDS nodes are energy efficient.

关键词： domination number non-split domination number detour number detour non-split domination number

Inequality of Nordhaus-Gaddum Type for Total Outer-connected domination in Graphs

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Acta Mathematica Sinica,English Series 2011年第3期27卷 607-616页

作者： Hong Xing JIANG Li Ying KANG College of Mathematics and Information Science Wenzhou University Wenzhou 325000 P. R. China Department of Mathematics Shanghai University Shanghai 200444 P. R. China

A set S of vertices in a graph G = （V, E） without isolated vertices is a total outer-connected dominating set （TCDS） of G if S is a total dominating set of G and G[V - S] is connected. The total outer-connected domination number of G, denoted by γtc（G）, is the minimum cardinality of a TCDS of G. For an arbitrary graph without isolated vertices, we obtain the upper and lower bounds on γtc（G）＋ γytc（G）, and characterize the extremal graphs achieving these bounds.

关键词： Graph domination number total outer-connected domination Nordhaus-Gaddum inequality

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

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