The Conditional Connectivity of Graphs

图的连通性是图论的一个基本研究课题，它与网络的可靠性（容错性）密切相关.图的经典的连通性是用连通度和 边连通度来度量的.图的连通度（边连通度）就是使图不连通所要删除的最小的点（边）数，显然它反映了相应的网络的容错性. 在通信网络的可靠性的进一步研究中，人们需要了解两个具有相同的连通度或边连通度的图，哪个可靠性更高？ 为了深入研究网络的可靠性或容错性，人们提出了许多条件连通性的概念. Harary在1983年引入条件连通度的概念\cite{2}.设图$G=(V，E)$，$P$是图的某种性质，S\subseteqV(G).$G$的条件连通度 $\kappa(G:P)$=min...The connectivity of graph is an element topic in the research of graph theory, it is closely related to the network reliability (fault tolerance). The classical connectivity concept of graph is connectivity and edge connectivity. Connectivity (edge connectivity) is the minimum number of vertices (edges) whose deletion makes the graph disconnected. Obviously, they reflect the corresponding net...学位：理学博士院系专业：数学科学学院数学与应用数学系_应用数学学号：1912008015045

λ′-最优图的充分条件

设G=(V,E)是一个连通图.边集SE,如果G-S不连通且G-S的每个连通分支至少有2个点,则称S是一个限制性边割.限制性边连通度λ′(G)就是G的最小限制性边割的基数.如果限制性边割存在,则称G是λ′-连通的.如果λ′(G)=ξ(G),则G是λ′-最优或者极大限制性边连通的,其中ξ(G)=min{|[X,Y]|:XV,|X|=2,G[X]连通}.图G的逆度是指R(G)=∑_v∈V 1/d(v).在此基础上,主要得到了:如果G是λ′-连通围长大于等于5的n阶图,且δ(G)≥2,如果R(G)小于某个关于最小度和顶点数的值,则G是λ′-最优的.对于不含钻石的图也得到了类似的结果.国家自然科学基金(11301440,11771362);;福建省中青年教师教育科研项目(JAT160350);;福建省自然科学基金(2015J05017

Sufficient Conditions for Graphs to Be Maximally 3-restricted Edge Connected

设g=(V,E)是一个连通图.如果λ3(g)=ξ3(g),则g是λ3-最优或者极大3-限制性边连通的,其中ξ3(g)=MIn{|[X,y]|:XV,|X|=3,g[X]连通}.g的逆度是指r(g)=∑_(V∈V)1/d(V).本文主要研究r(g)与顶点数n,最小度δ及ξ3的关系,并由此得到一函数,用这一函数来限制r(g),使g是λ3-最优的.Let G=(V,E) be a connected graph.A graph G is called λ3-optimal,if λ3(G),where ξ3(G)=min{||:XV,|X|=3,G[X] is connected}.In this paper,we study the relation between R(G) and vertex number n,minimum degree δ,ξ3,and obtain a function.If R(G) is not more than the function,then G is λ3-optimal.国家自然科学基金项目(10831001;11026183);福建省教育厅科研项目(JA10021

Sufficient Conditions for λ_3-Optimality of Triangle-Free Graphs

设G=(V,E)是一个连通图,边集S(?)E是一个3-限制性边割,如果G-S是不连通的并且G-S的每个分支至少有三个点.图G的3-限制性边连通度λ_3(G)是G中最小的一个3-限制性边割的基数.图G是λ_3(G)连通的,如果3-限制性边割存在.G是λ_3-最优的,如果λ_3(G)=ξ_3(G),其中ξ_3(G)=min{|[U,(?)]|:U(?)V,|U|=3 and G[U]是连通的).G[U]表示V的子集U的导出子图,(?)=V\U表示U的补.[U,(?)]是一条边的一个端点在U中另一个端点在(?)中的边的集合.本文给出了不含三角形的图是λ_3-最优的一些充分条件.Let G=(V,E) be a connected graph.An edge set S(?)E is a 3-restricted- edge-cut,if G-S is disconnected and every component of G-S has at least three vertices. The 3-restricted-edge-connectivityλ_3(G) of G is the cardinality of a minimum 3-restricted- edge-cut of G.A graph G isλ_3-connected,if 3-restricted-edge-cuts exist.A graph G is calledλ_3-optimal,ifλ_3(G)=ξ_3(G),whereξ_3(G)=min{|[U,(?)]|:U(?)V,|U|=3 and G[U]is connected}.G[U]is the subgraph of G induced by the vertex subset U(?)V,and (?)=V\U is the complement of U.[U,(?)]is the set of edges with one end in U and the other in U.In this paper,we give some sufficient conditions for triangle-free graphs to beλ_3-optimal.supported by NSFC (No.10671165);; XJEDU (No.2004G05)

Connectivity of n-double Graphs

设g_1=(V_1,E_1),g_2=(V_2,E_2)是两个连通图,直积(dIrECT PrOduCT)(也称为krOnECkEr PrOduCT,TEnSOr PrOduCT和CrOSS PrOduCT)g_1g_2的点集为V(g_1g_2)=V(g_1)V(g_2),边集为E(g_1g_2)={(u_1,V_1)(u_2,V_2):u_1u_2∈E(g_1),V_1V_2∈E(g_2)).简单图g的n-dOublE图d_n[g]=gT_n,其中n个点的全关系图T_n是完全图k_n在每个点加上一个自环得到的图.在本文中,我们研究了d_n[g]的(边)连通性,超(边)连通性.Let G =(V,E) be a connected graph.The direct product(also named Kronecker product,tensor product and cross product) G_1×G_2 has vertex set V(G_1×G_2)= V(G_1)×V(G_2) and edge set E(G_1×G_2) = {(u_1,v_1)(u_2,v_2):u_1u_2∈E(G_1),v_1v_2∈E(G_2)}.We define the n-double of a simple graph G as the graph D_n[G]= G×T_n.The total graph T_n on n vertices is the graph associated to the total relation(where every vertex is adjacent to every vertex).It can be obtained from the complete graph K_n by adding a loop to every vertex.In this paper,we study the(edge)connectivity,super(edge)connectivity of D_n[G].国家自然科学基金(11171279;11126321;11161006;71201049); 厦门理工学院博士启动金(YKJ12030R); 广西自然科学基金(2012GXNSFBA053005)资助项

不锈钢酸洗废水钙钠中和沉淀与碳热还原协同处理新工艺

通过研究不锈钢酸洗废水体系中氟离子脱除和金属离子沉淀的规律,开发了钙钠协同沉淀新工艺,并对新工艺产生的污泥于1200℃下进行还原,细磨、磁选后得铁、铬、镍合金粉末和再生萤石矿。结果表明,该工艺实现了废水的达标排放,污泥产生量减少了14.79%,实现了铁铬镍的金属化还原,得到了再生萤石矿和金属品位93.62%的合金粉末,合金粉末中铁、铬、镍品位分别达69.31%, 7.60%和16.71%,回收率分别高达95.30%, 88.70%和97.53%

不锈钢酸洗废水钙钠中和沉淀与碳热还原协同处理新工艺

通过研究不锈钢酸洗废水体系中氟离子脱除和金属离子沉淀的规律,开发了钙钠协同沉淀新工艺,并对新工艺产生的污泥于1200℃下进行还原,细磨、磁选后得铁、铬、镍合金粉末和再生萤石矿。结果表明,该工艺实现了废水的达标排放,污泥产生量减少了14.79%,实现了铁铬镍的金属化还原,得到了再生萤石矿和金属品位93.62%的合金粉末,合金粉末中铁、铬、镍品位分别达69.31%, 7.60%和16.71%,回收率分别高达95.30%, 88.70%和97.53%

不锈钢酸洗废水钙钠中和沉淀与碳热还原协同处理新工艺

通过研究不锈钢酸洗废水体系中氟离子脱除和金属离子沉淀的规律,开发了钙钠协同沉淀新工艺,并对新工艺产生的污泥于1200℃下进行还原,细磨、磁选后得铁、铬、镍合金粉末和再生萤石矿。结果表明,该工艺实现了废水的达标排放,污泥产生量减少了14.79%,实现了铁铬镍的金属化还原,得到了再生萤石矿和金属品位93.62%的合金粉末,合金粉末中铁、铬、镍品位分别达69.31%, 7.60%和16.71%,回收率分别高达95.30%, 88.70%和97.53%

Effect of N Fertilizer Application on the Nitrate Accumulation in Garden Mass and Soil under Facility Agriculture

采用田间实验研究了施用氮肥对设施条件下大青菜生长发育和产量,以及对土壤硝酸盐含量累积分布的影响。结果表明,在施氮肥0~500 kg hm-2范围内,氮肥施用量越大,产量越高,但到达一定量时,便不能再促进产量的提高,反而会引起减产。土壤铵态氮含量随着土壤剖面向下不断下降,表层的铵态氮含量较高,土壤硝态氮含量在整个土壤剖面的分布变化较小,但也是从表层向下处于一种缓慢减少的趋势,铵态氮的累积主要集中在上部土壤剖面,硝态氮的累积分布在整个土壤剖面,土壤硝态氮含量随施肥量增加而增加;氮肥施用量对硝酸盐含量有很大影响。在施氮肥0~700kg hm-2范围内,氮肥施用量越多,大青菜硝酸盐含量越高