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The General Facility Location Problem with Connectivity on Trees

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Acta Mathematica Sinica,English Series 2016年第9期32卷 1106-1112页

作者： er fang shan Li Ying KANG School of Management Shanghai University Shanghai 200444 P. R. China Department of Mathematics Shanghai University Shanghai 200444 P. R. China

In this note we study the general facility location problem with connectivity. We present an O（np2）-time algorithm for the general facility location problem with connectivity on trees. Furthermore,we present an O（n... 详细信息

关键词： Connected p-center connected p-median tree equivalent binary tree

Sufficient Conditions for Maximally Edge-Connected Hypergraphs

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Journal of the Operations Research Society of China 2021年第1期9卷 119-129页

作者： Lin-Ken Tong er-fang shan Department of Mathematics Shanghai UniversityShanghai 200444China School of Management Shanghai UniversityShanghai 200444China

The edge-connectivity of a graph or a hypergraph is defined as the minimum number of edges whose removal renders the graph or hypergraph disconnected.A graph or hypergraph is called maximally edge-connected if the edge-connectivity equals its minimum *** this paper,we show that some classical sufficient conditions for graphs to be maximally edge-connected can be generalized to hypergraphs.

关键词： Hypergraph Edge-connectivity Maximally edge-connected

The Myerson Value on Local Structures of Coalitions

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Journal of the Operations Research Society of China 2019年第3期7卷 461-473页

作者： Daniel LiLi er-fang shan School of Management Shanghai UniversityShanghai 200444China

The Myerson value introduced by Mayerson(Math Oper Res 2:225-229,1977)is a solution for cooperative games under the partial cooperation structures described by graphs,in which feasible coalitions are connected but their structures are *** extend the Myerson value,we define a mapping to describe local structures of coalitions and obtain a new solution for cooperative games,called Myerson value with local *** propose an ax iomatic characterization of the Myerson value associated with local cooperative structures.

关键词： Cooperative game Myerson value Graph game TU game Local structure

The Maximum α-spectral Radius of Unicyclic Hypergraphs with Fixed Diameter

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Acta Mathematica Sinica,English Series 2022年第5期38卷 924-936页

作者： Li Ying KANG Jing WANG er fang shan Department of Mathematics Shanghai UniversityShanghai 200444P.R.China School of Management Shanghai UniversityShanghai 200444P.R.China

For 0≤α<1,theα-spectral radius of an r-uniform hypergraph G is the spectral radius of A_(α)(G)=αD(G)+(1-α)A(G),where D(G)and A(G)are the diagonal tensor of degrees and adjacency tensor of G,*** this paper,we sho... 详细信息

For 0≤αergraph G is the spectral radius of A_(α)(G)=αD(G)+(1-α)A(G),where D(G)and A(G)are the diagonal tensor of degrees and adjacency tensor of G,*** this paper,we show the perturbation ofα-spectral radius by contracting an *** we determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with fixed *** also determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with given number of pendant edges.

关键词： Unicyclic hypergraph α-spectral radius principal eigenvector diameter pendant edge

On the Clique-Transversal Number in(Claw,K_4 )-Free 4-Regular Graphs

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Acta Mathematica Sinica,English Series 2014年第3期30卷 505-516页

作者： Ding Guo WANG er fang shan Zuo Song LIANG Department of Mathematics Shanghai University College of Mathematics Science Chongqing Normal University School of Management Shanghai University

A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of *** clique-transversal number,denoted by τC（G）,is the minimum cardinality of a clique-transversal set in *** this paper,we first present a lower bound on τC（G） and characterize the extremal graphs achieving the lower bound for a connected（claw,K4）-free 4-regular graph ***,we show that for any 2-connected（claw,K4）-free 4-regular graph G of order n,its clique-transversal number equals to [n/3].

关键词： Graph clique-transversal set clique 4-regular graph claw-free graph

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

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

Upper Locating-Domination Numbers of Cycles

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Journal of Mathematical Research and Exposition 2011年第4期31卷 757-760页

作者： Yan Cai ZHAO er fang shan Ru Zhao GAO Foundation Department Wuxi City College of Vocational Technology Jiangsu 214153 P. R. China Department of Mathematics Shanghai University Shanghai 200444 P. R. China Department of Mathematics and Physics Bengbu College Anhui 233030 P. R. China

A set D of vertices in a graph G = （V, E） is a locating-dominating set （LDS） if for every two vertices u, v of V ／ D the sets N（u） ∩D and N（v） ∩ D are non-empty and different. The locating-domination number γL（G） is the minimum cardinality of an LDS of G, and the upper-locating domination number FL（G） is the maximum cardinality of a minimal LDS of G. In the present paper, methods for determining the exact values of the upper locating-domination numbers of cycles are provided.

关键词： locating-domination number upper locating-domination number cycle

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无向路图和块图上的混合控制

数学学报（中文版） 2017年第4期60卷 641-650页

作者：赵衍才单而芳王海超无锡城市职业技术学院无锡214153 上海大学管理学院上海200444 上海电力学院上海200090

图G=(V,E)的一个混合控制集是一个满足如下条件的集合DV∪E:不在D中的每个点或每条边都相邻或关联于D中的至少一个点或一条边.确定图的最小基数的混合控制集的问题称为混合控制问题.本文研究混合控制问题的算法复杂性,证明了混合控制... 详细信息

图G=(V,E)的一个混合控制集是一个满足如下条件的集合DV∪E:不在D中的每个点或每条边都相邻或关联于D中的至少一个点或一条边.确定图的最小基数的混合控制集的问题称为混合控制问题.本文研究混合控制问题的算法复杂性,证明了混合控制问题在无向路图上是NP-完全的,但在块图上有线性时间算法.无向路图和块图都是弦图的子类,又是树的母类.

关键词：混合控制无向路图块图算法 NP-完全性