1.

关于广义Petersen图的紧致性的注记





赵中云 韩绍岑《数学研究与评论》,1992年第12卷第2期


We show that, for each integer n ≥ 5, the toughness of a generalized Petersen graph with 2n vertices is less than or equal to 4/3, and 4/3 is the best upper bound.

2.

三边连通超欧拉图的一个注记





李宵民 李登信《数学研究及应用》,2010年第30卷第5期


For two integers l ：〉 0 and k ≥ 0, define C（l, k） to be the family of 2edge connected graphs such that a graph G ∈ C（l, k） if and only if for every bond S lohtain in E（G） with ｜S｜ ≤3, each component of G  S has order at least （｜V（G）｜  k）/l. In this note we prove that if a 3 edgeconnected simple graph G is in C（10, 3）, then G is supereulerian if and only if G cannot be contracted to the Petersen graph. Our result extends an earlier result in [Supereulerian graphs and Petersen graph. JCMCC 1991, 9： 7989] by Chen.

3.

On the Constant Metric Dimension of Generalized Petersen Graphs P（n, 4）





Saba NAZ Muhammad SALMAN Usman ALI Imran JAVAID Syed AhtshamulHaq BOKHARY《数学学报(英文版)》,2014年第30卷第7期


In this paper, we consider the family of generalized Petersen graphs P（n,4）. We prove that the metric dimension of P（n, 4） is 3 when n = 0 （mod 4）, and is 4 when n = 4k ＋ 3 （k is even）.For n = 1,2 （mod 4） and n = 4k ＋ 3 （k is odd）, we prove that the metric dimension of P（n,4） is bounded above by 4. This shows that each graph of the family of generalized Petersen graphs P（n, 4） has constant metric dimension.

4.

Synchronization of networks with timevarying couplings





Wenlian Lu Tianping Chen《高校应用数学学报(英文版)》,2013年第28卷第4期


In this paper, we present a review of our recent works on complete synchronization analyses of networks of the coupled dynamical systems with timevarying couplings. The main approach is composed of algebraic graph theory and dynamic system method. More precisely, the Hajnal diameter of matrix sequence plays a key role in investigating synchronization dynamics and the joint graph across time periods possessing spanning tree is a doorsill for timevarying topologies to reach synchronization. These techniques with proper modification count for diverse models of networks of the coupled systems, including discretetime and continuoustime models, linear and nonlinear models, deterministic and stochastic timevariations. Alternatively, transverse stability analysis of general timevarying dynamic systems can be employed for synchronization study as a special case and proved to be equivalent to Hajnal diameter.

5.

Supereulerian graphs and the Petersen graph





Xiao Min Li Lan Lei HongJian Lai Meng Zhang《数学学报(英文版)》,2014年第30卷第2期


A graphG is supereulerian if G has a spanning eulerian subgraph.Boesch et al.[J.Graph Theory,1,79–84（1977）]proposed the problem of characterizing supereulerian graphs.In this paper,we prove that any 3edgeconnected graph with at most 11 edgecuts of size 3 is supereulerian if and only if it cannot be contractible to the Petersen graph.This extends a former result of Catlin and Lai[J.Combin.Theory,Ser.B,66,123–139（1996）].

6.

将小直径图划分为导出匹配





杨爱峰 原晋江《高校应用数学学报(英文版)》,2004年第19卷第3期


Given a simple graph G and a positive integer k, the induced matching kpartition problem asks whether there exists a kpartition (V1,V2,…Vk)of V(G) such that for each i(1≤i≤k),G[Vi] is 1 regular. This paper studies the computational complexity of this problem for graphs with small diameters. The main results are as follows: Induced matching 2partition problem of graphs with diameter 6 and induced matching 3partition problem of graphs with diameter 2 are NP complete;induced matching 2partition problem of graphs with diameter 2 is polynomially solvable.

7.

Convergence of Online Gradient Method with Penalty for BP Neural Networks





Shao Hongmei Wu Wei Liu Lijun《东北数学》,2010年第26卷第1期


Online gradient method has been widely used as a learning algorithm for training feedforward neural networks. Penalty is often introduced into the training procedure to improve the generalization performance and to decrease the magnitude of network weights. In this paper, some weight boundedness and deterministic con vergence theorems are proved for the online gradient method with penalty for BP neural network with a hidden layer, assuming that the training samples are supplied with the network in a fixed order within each epoch. The monotonicity of the error function with penalty is also guaranteed in the training iteration. Simulation results for a 3bits parity problem are presented to support our theoretical results.

8.

Are networks with more edges easier to synchronize,or not？





段志生 王文旭 刘超 陈关荣《中国物理 B》,2009年第18卷第8期


In this paper,the relationship between network synchronizability and the edgeaddition of its associated graph is investigated.First,it is shown that adding one edge to a cycle definitely decreases the network synchronizability.Then,since sometimes the synchronizability can be enhanced by changing the network structure,the question of whether the networks with more edges are easier to synchronize is addressed.Based on a subgraph and complementary graph method,it is shown by examples that the answer is negative even if the network structure is arbitrarily optimized.This reveals that generally there are redundant edges in a network,which not only make no contributions to synchronization but actually may reduce the synchronizability.Moreover,a simple example shows that the node betweenness centrality is not always a good indicator for the network synchronizability.Finally,some more examples are presented to illustrate how the network synchronizability varies following the addition of edges,where all the examples show that the network synchronizability globally increases but locally fluctuates as the number of added edges increases.

9.

Maximum Genus of Strong Embeddings 被引次数：4





ErlingWei YanpeiLiu HanRen《应用数学学报(英文版)》,2003年第19卷第3期


The strong embedding conjecture states that any 2connected graph has a strong embedding on some surface. It implies the circuit double cover conjecture: Any 2connected graph has a circuit double cover.Conversely, it is not true. But for a 3regular graph, the two conjectures are equivalent. In this paper, a characterization of graphs having a strong embedding with exactly 3 faces, which is the strong embedding of maximum genus, is given. In addition, some graphs with the property are provided. More generally, an upper bound of the maximum genus of strong embeddings of a graph is presented too. Lastly, it is shown that the interpolation theorem is true to planar Halin graph.

10.

A characterization of PMcompact Hamiltonian bipartite graphs





Xiumei WANG Jinjiang YUAN Yixun LIN《应用数学学报(英文版)》,2015年第31卷第2期


The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings in G. A graph is called perfect matching compact(shortly, PMcompact), if its perfect matching polytope has diameter one. This paper gives a complete characterization of simple PMcompact Hamiltonian bipartite graphs. We first define two families of graphs, called the H2Cbipartite graphs and the H23bipartite graphs, respectively. Then we show that, for a simple Hamiltonian bipartite graph G with V(G) ≥ 6, G is PMcompact if and only if G is K3,3, or G is a spanning Hamiltonian subgraph of either an H2Cbipartite graph or an H23bipartite graph.

11.

GENERALIZED AIRY FUNCTIONS WITH COMPLEX VARIABLES





李家春 赵大刚《应用数学和力学(英文版)》,1985年第6卷第11期


In the present paper,we have made a detailed study of the generalized Airy functions,which have found wide applications in the field of wave propagation and hydrodynamicstability.A series of tables and graphs are provided for the above functions with complexvariables.The results are proved satisfactory.

12.

ON kDIAMETER OF kCONNECTED GRAPHS





XuJunming XuKeli《高校应用数学学报(英文版)》,2001年第16卷第3期


Abstract. Let G be a kconnected simple graph with order n. The kdiameter, combining connectivity with diameter, of G is the minimum integer

13.

Bipartite Version of the Erd?sSós Conjecture





Xinmin HOU Chenhui Lü《数学研究及应用》,2019年第3期


The Erd?sSós Conjecture states that every graph on n vertices and more than n(k2)/2 edges contains every tree of order k as a subgraph. In this note, we study a weak(bipartite)version of Erd?sSós Conjecture. Based on a basic lemma, we show that every bipartite graph on n vertices and more than n(k2)/2 edges contains the following families of trees of order k:(1) trees of diameter at most five;(2) trees with maximum degree at least [k1/2];(3) almost balanced trees, these results are better than the corresponding known results for the general version of the Erd?sSós Conjecture.

14.

The effects of degree correlations on network topologies and robustness





赵 静 陶 林 俞 鸿 骆建华 曹志伟 李亦学《中国物理》,2007年第16卷第12期


Complex networks have been applied to model numerous interactive nonlinear systems in the real world. Knowledge about network topology is crucial to an understanding of the function, performance and evolution of complex systems. In the last few years, many network metrics and models have been proposed to investigate the network topology, dynamics and evolution. Since these network metrics and models are derived from a wide range of studies, a systematic study is required to investigate the correlations among them. The present paper explores the effect of degree correlation on the other network metrics through studying an ensemble of graphs where the degree sequence （set of degrees） is fixed. We show that to some extent, the characteristic path length, clustering coefficient, modular extent and robustness of networks are directly influenced by the degree correlation.

15.

3阶幂图的广义导出匹配可扩性





吴龙树 闫运生 王勤《数学研究及应用》,2010年第30卷第3期


A graph G is induced matching extendable if every induced matching of G is included in a perfect matching of G. A graph G is generalized induced matching extendable if every induced matching of G is included in a maximum matching of G. A graph G is clawfree, if G dose not contain any induced subgraph isomorphic to K1,3. The kth power of G, denoted by Gu, is the graph with vertex set V（G） in which two vertices are adjacent if and only if the distance between them is at most k in G. In this paper we show that, if the maximum matchings of G and G3 have the same cardinality, then G3 is generalized induced matching extendable. We also show that this result is best possible. As a result, we show that if G is a connected clawflee graph, then G3 is generalized induced matching extendable.

16.

Minimum congestion spanning trees in bipartite and random graphs





M.I. Ostrovskii《数学物理学报(B辑英文版)》,2011年第31卷第2期


The first problem considered in this article reads: is it possible to find upper estimates for the spanning tree congestion in bipartite graphs, which are better than those for general graphs? It is proved that there exists a bipartite version of the known graph with spanning tree congestion of order n 3 2 , where n is the number of vertices. The second problem is to estimate spanning tree congestion of random graphs. It is proved that the standard model of random graphs cannot be used to find graphs whose spanning tree congestion has order greater than n 3 2 .

17.

A structural theorem on embedded graphs and its application to colorings





Bao Gang Xu Xiao Xu Lu《数学学报(英文版)》,2009年第25卷第1期


In this paper, a Lebesgue type theorem on the structure of graphs embedded in the surface of characteristic σ≤ 0 is given, that generalizes a result of Borodin on plane graphs. As a consequence, it is proved that every such graph without icircuits for 4 ≤ i ≤ 11  3σ is 3choosable, that offers a new upper bound to a question of Y. Zhao.

18.

On kcritical 2kconnected graphs





苏健基 袁旭东 赵巧凤《中国科学A辑(英文版)》,2003年第46卷第3期


A graph G is called an (n, k)graph if k(G  S) = n  S for any S V(G) with S ≤ k, where k.(G) denotes the connectivity of G. Mader conjectured that for k ≥ 3 the graph K2k+2  (1factor) is the unique (2k, k)graph. Kriesell has settled two special cases for k = 3, 4. We prove the conjecture for the general case k ≥ 5.

19.

Results of the maximum genus of graphs





Guanghua DONG~ Yanpei LIU Department of Mathematics School of Science Beijing Jiaotong University Beijing 100044 China《中国科学A辑(英文版)》,2007年第50卷第11期


In this paper,we provide a new class of upembeddable graphs,and obtain a tight lower bound on the maximum genus of a class of 2connected pseudographs of diameter 2 and of a class of diameter 4 multigraphs.This extends a result of Skoviera.

20.

本刊英文版Vol.31(2015),No.4论文摘要（英文）





《数学学报》,2015年第3期


Nonorientable Genera of Petersen Powers Wen Zhong LIU Ting Ru SHEN Yi Chao CHEN Abstract In the paper,we prove that for every integern≥1,there exists a Petersen power P~n with nonorientable genus and Euler genus precisely n.which improves the upper bound of Mohar and Vodopivec’s result[J.Graph Theory,67,18(2011)]that for every integer k(2≤k≤n1),a Petersen power P~n exists with nonorientable genus and Euler genus precisely k.Polynomials with Palindromic and Unimodal Coefficients
