Upper and lower bounds for the energy of bipartite graphs

Using Lagrange's multiplier rule, we find upper and lower bounds of the energy of a bipartite graph G, in terms of the number of vertices, edges and the spectral moment of fourth order. Moreover, the upper bound is attained in a graph G if and only if G is the graph of a symmetric balanced incomplete block design (BIBD). Also, we determine the graphs for which the lower bound is sharp.     

2‐connected 7‐coverings of 3‐connected graphs on surfaces

An m‐covering of a graph G is a spanning subgraph of G with maximum degree at most m. In this paper, we shall show that every 3‐connected graph on a surface with Euler genus k ≥ 2 with sufficiently large representativity has a 2‐connected 7‐covering with at most 6k ? 12 vertices of degree 7. We also construct, for every surface F² with Euler genus k ≥ 2, a 3‐connected graph G on F² with arbitrarily large representativity each of whose 2‐connected 7‐coverings contains at least 6k ? 12 vertices of degree 7. © 2003 Wiley Periodicals, Inc. J Graph Theory 43: 26–36, 2003     

B值随机变量阵列加权和的完全收敛性

设{X_ni:1≤i≤n,n≥1}为行间独立的B值r.v.阵列,g(z)是指数为1/p的正则变化函数,r>0,{ani 1≤t≤n,n≥1}为实数阵列,本文得到了使(?)成立的条件,推广并改进了Stout及Sung等的著名结论.     

关于Pn3的优美性

设G(V,E)是一个简单图,对自然数k,当V(G^k)=V(G,E(G^k)=E(G)∪{uv|d(u,v)=k},则称图G^k为k-次方图,本文证明了图P_n³的优美性。     

纵横扩张的优化

得到了最小折数纵横扩张的判别准则．针对4-正则图的平面嵌入的纵横扩张的特殊性，给出了它的最小折数纵横扩张判别准则．     

关于带宽极值问题的一些结果

本文研究的问题是确定f(p,B）的值，也就是给定顶点数p和带宽B，求满足最大度不超过B的连通图的最小边数，本文给出了一些f(p,B）的值及相应极图。     

Submanifolds associated with graphs

In this paper we present an interesting relationship between graph theory and differential geometry by defining submanifolds of almost Hermitian manifolds associated with certain kinds of graphs. We show some results about the possibility of a graph being associated with a submanifold and we use them to characterize CR-submanifolds by means of trees. Finally, we characterize submanifolds associated with graphs in a four-dimensional almost Hermitian manifold.

     

直径不超过4的树的割宽

§ 1　IntroductionThe cutwidth problem for graphs,as well as a class of optimal labeling and embed-ding problems,have significant applications in VLSI designs,network communicationsand other areas (see [2 ] ) .We shall follow the graph-theoretic terminology and notation of [1 ] .Let G=(V,E)be a simple graph with vertex set V,| V| =n,and edge set E.A labeling of G is a bijec-tion f:V→ { 1 ,2 ,...,n} ,which can by regarded as an embedding of G into a path Pn.Fora given labeling f of G,th…     

凸度量空间中单值和集值映象的公共不动点定理

§ 1.　Introduction　　Anecessaryandsufficientconditionandasufficientconditiontoensurethataset valuedmappingandasingle valuedmappinginacompletemetricspaceandacompleteconvexmetricspacehavingacommonfixedpointarerespectivelygivenin [1 ] .Meanwhilethemainresultsin[2 ]— [5]areimprovedandextendedin [1 ] .Inthispaper ,theexistenceatcommonfixedpointsoftwoset valuedmappingandasing valuedmappingwerestudied ,andthecorrespond ingresultsin [1 ]— [5]wereextendedandimproved .Let(X ,d)beanon emptymetricspa…     

单圈图的最大特征值序

主要讨论了单圈图按其最大特征值进行排序的问题，确定了该序的前六个图。