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,respectively.In th...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,respectively.In this paper,we show the perturbation ofα-spectral radius by contracting an edge.Then we determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with fixed diameter.We also determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with given number of pendant edges.展开更多
A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G.The clique-transversal number,denoted by τC（G）,is the minimum cardinality of a clique-transversal set in G.In thi...A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G.The clique-transversal number,denoted by τC（G）,is the minimum cardinality of a clique-transversal set in G.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 G.Furthermore,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].展开更多
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...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（np）-time algorithm for the general facility location problem with connectivity on equivalent binary trees.展开更多
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 ...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.展开更多
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...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.展开更多
基金Supported by the National Nature Science Foundation of China(Grant Nos.11871329,11971298)。
文摘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,respectively.In this paper,we show the perturbation ofα-spectral radius by contracting an edge.Then we determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with fixed diameter.We also determine the unique unicyclic hypergraph with the maximumα-spectral radius among all r-uniform unicyclic hypergraphs with given number of pendant edges.
基金Supported by National Nature Science Foundation of China(Grant Nos.11171207 and 10971131)
文摘A clique-transversal set D of a graph G is a set of vertices of G such that D meets all cliques of G.The clique-transversal number,denoted by τC（G）,is the minimum cardinality of a clique-transversal set in G.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 G.Furthermore,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].
基金Supported by National Nature Science Foundation of China(Grant Nos.11471210,11571222)
文摘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（np）-time algorithm for the general facility location problem with connectivity on equivalent binary trees.
基金supported by Korea Research Foundation Grant (KRF-2002-015-cp0050)the National Natural Science Foundation of China (Grant Nos. 60773078, 10571117)+3 种基金the ShuGuang Plan of Shanghai Education Development Foundation (Grant No. 06SG42)M. A. Henning is supported in part by the South African National Research Foundationthe University of KwaZulu-Natalsupported by Shanghai Leading Academic Discipline Project (No. $30104)
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant No.60773078)the Natural Science Foundation of Anhui Provincial Education Department (No.KJ2011B090)
文摘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.
