环状硅酸盐图的友好指数集

Let G be a graph with vertex set V(G) and edge set E(G). A labeling f : V(G) →Z2 induces an edge labeling f*: E(G) → Z2 defined by f*(xy) = f(x) + f(y), for each edge xy ∈ E(G). For i ∈ Z2, let vf(i) = |{v ∈ V(G) : f(v) = i}| and ef(i) = |{e ∈ E(G) : f*(e) =i}|. A labeling f of a graph G is said to be friendly if |vf(0)- vf(1)| ≤ 1. The friendly index set of the graph G, denoted FI(G), is defined as {|ef(0)- ef(1)|: the vertex labeling f is friendly}. This is a generalization of graph cordiality. We investigate the friendly index sets of cyclic silicates CS(n, m).     

Minor and minimum cycle bases of a 3-connected planar graph

In this paper, we prove that if any set of ｜E（G）｜- ｜V（G）｜ ＋ 1 facial cycles of a 3-connected planar graph G embedded in the plane doesn＇t form a minimum cycle base of G, then any minimum cycle base of G contains a separating cycle, and G has a minor isomorphic to T6, where T6 is the graph obtained from the complete graph K6 by deleting a path with four edges.     

On product-cordial index sets and friendly index sets of 2-regular graphs and generalized wheels

A vertex labeling f : V → Z2 of a simple graph G = (V, E) induces two edge labelings f+ , f*: E → Z2 defined by f+ (uv) = f(u)+f(v) and f*(uv) = f(u)f(v). For each i∈Z2 , let vf(i) = |{v ∈ V : f(v) = i}|, e+f(i) = |{e ∈ E : f+(e) = i}| and e*f(i)=|{e∈E:f*(e)=i}|. We call f friendly if |vf(0)-vf(1)|≤ 1. The friendly index set and the product-cordial index set of G are defined as the sets{|e+f(0)-e+f(1)|:f is friendly} and {|e*f(0)-e*f(1)| : f is friendly}. In this paper we study and determine the connection between the friendly index sets and product-cordial index sets of 2-regular graphs and generalized wheel graphs.     

符号混合控制问题的某些NP-完全性结果

Let G =(V, E) be a simple graph with vertex set V and edge set E. A signed mixed dominating function of G is a function f:V∪E→ {-1, 1} such that ∑_(y∈N_m(x)∪{x})f(y)≥ 1for every element x∈V∪E, where N_m(x) is the set of elements of V∪E adjacent or incident to x. The weight of f is w(f) =∑_(x∈V∪E)f(x). The signed mixed domination problem is to find a minimum-weight signed mixed dominating function of a graph. In this paper we study the computational complexity of signed mixed domination problem. We prove that the signed mixed domination problem is NP-complete for bipartite graphs, chordal graphs, even for planar bipartite graphs.     

Z3-CONNECTIVITY OF 4-EDGE-CONNECTED TRIANGULAR GRAPHS

A graph G is k-triangular if each of its edge is contained in at least k triangles. It is conjectured that every 4-edge-connected triangular graph admits a nowhere-zero 3-flow. A triangle-path in a graph G is a sequence of distinct triangles T_1 T_2··· T_k in G such that for 1 ≤ i ≤ k-1, |E(T_i) ∩ E(T_(i+1))| = 1 and E(T_i) ∩ E(T_j) = ? if j i + 1. Two edges e, e′∈ E(G) are triangularly connected if there is a triangle-path T_1, T_2, ···, T_k in G such that e ∈ E(T_1)and e′∈ E(T_k). Two edges e, e′∈ E(G) are equivalent if they are the same,parallel or triangularly connected. It is easy to see that this is an equivalent relation. Each equivalent class is called a triangularly connected component.In this paper, we prove that every 4-edge-connected triangular graph G is Z_3-connected, unless it has a triangularly connected component which is not Z_3-connected but admits a nowhere-zero 3-flow.     

On the elusiveness of Hamiltonian property

1. IntroductionA gash G is an ordered pair of disjoillt sets (V, E) such that E is a subset of the setof unordered pairs of V, where the sets V and E are finite. The set V is cajled the setof venices and E is called the set of edges. They are usually denoted by V(G) and E(C),respectively. An edge (x, y) is said to join the venices x and y, and is sometimes denotedby xo or ear. By our definition, a graph does not colltain any loOP, neither does it colltainmultiple edges.Other terms undef…     

完全图与完全n部图的完全多部图分解

§ 1　IntroductionLet V(G) and E(G) be the vertex setand the edge setof a graph G,respectively.Fori=1 ,...,p,if V(Gi) V(G) ,E(Gi)∩ E(Gj) = for i≠ j,and∪pi=1 E(Gi) =E(G) ,then wecall{ G1 ,...,GP} a decomposition of G.Let[i,j] be the integer interval including i and j.Let Knbe a complete graph with the vertex set[1 ,n] .For m disjointsubsets A1 ,...Amof[1 ,n] ,let K(A1 ,...,Am) be a complete m-partite graph having partite-sets A1 ,...,Am.If| Ai| =1 ,Ai is called a S-set;otherwi…     

Panconnectivity for interconnection networks with faulty elements

Let Go and G1 be two graphs with the same vertices. The new graph G（G0, G1; M） is a graph with the vertex set V（0o） ∪）V（G1） and the edge set E（Go） UE（G1） UM, where M is an arbitrary perfect matching between the vertices of Go and G1, i.e., a set of cross edges with one endvertex in Go and the other endvertex in G1. In this paper, we will show that if Go and G1 are f-fault q-panconnected, then for any f 〉 2, G（G0, G1; M） is （f ＋ 1）-fault （q ＋ 2）-panconnected.     

Full friendly index sets of Cartesian products of two cycles

Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊ ： E → Z2 defined by f＊（xy） = f（x） ＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i） = ｜f＊^-1（i）｜. A labeling f is called friendly if ｜vf（1） - vf（0）｜ ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if（G） = e（1） - el（0）. The set [if（G） ｜ f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI（G）. In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.     

HAMILTONIAN DECOMPOSITION OF CAYLEY GRAPHS OF ORDERS p~2 AND pq

1. IntroductionLet G be a finite group and S a subset of G such that S--1 ~ S, and 1 f S. The Cayleygraph Cay (G, S) is defined as the simple graph with V ~ G, and E = {glgZ I g,'g, or g,'g,6 S, gi, gi E G}. Cay (G, S) is vertex-transitive, and it is connected if and only if (S) = G,i.e. S is a generating set of G[1]. If G = Zn, then Cay (Zn, S) is called a circulant graph. Ithas been proved that any connected Cayley graph on a finite abelian group is hamiltonianl2].Furthermore, …     

一类矩阵的AOR迭代收敛性分析及其与SOR迭代的比较

1 引言 许多实际问题最后常归结为解一个或一些矩阵的线性代数方程组Ax=b （1.1）这里讨论A为（1，1）相容次序矩阵的情形。     

双模范畴间同构态射的构造

本文研究了双模范畴上的同构态射.利用代数上常用的构造方法,给出了模范畴R(C:T)和L(C:T)的定义及双模范畴TMC和TMCM之间的同构映射和证明过程,将代数上双模范畴的一些重要结论进行了推广.     

半序集的碰撞数与分层深度贪婪算法

设Ｐ＝（Ｘ，≤）是一个半序集，本文在关于碰撞数的深度贪婪算法的基础上，直接证明了对任意的Ｐ存在一个最优的ＤＬＧ扩张，给出了ＤＬＧ半序集的定义，并证明了半序集Ｐ是ＤＬＧ半序集的一个充分条件，最后给出了ＤＬＧ扩张算法。     

非齐次空间上的奇异积分交换子的有界性

本文在非齐次空间上给出了交换子[b,T](f)=bTf(x)-T(bf)(x)在b(x)是Lipschitz函数时的 Lp(p>1)有界性.     

关于“停走”生成器概率模型中的符合率问题

本文首先建立了“停走”生成器辅出序列的概率模型,给出了“停走”生成器输出序列与其线性移位寄存器序列之间的符合率的计算公式。     

THE SOLUTION TO THE SK-MODEL

IIntroductlonAs one ofwell－kn。mean ield models for spin glasses,the SK(Sherrin红on－Kirkpatri山)model has been studied by many authors恤叫2]nd[81,andthe references therein)．Particu－larl儿丁劝a以andls]repm眈* some quite lmerestingresults on It in his one－hour Invited talk tthe International Congress ofMathem航icians held t Berlin in August,ig98．In mathematical terms;the SK－Model Is the study of a cert。n random measure on Z。:＝{一1;1}”for a natural。mber N．Z。Is called configu…     

经济最优化意义下消耗系数的调整

本文基于“正特片矢量法”,提出了一种在经济最优化意义下调整消耗系数的方法.该方法能够综合考虑产综和价格对消耗系数的影响,有着较好的普适性,在计算上简便易行、效果良好,且具有明显的经济意义.     

非齐次空间上的奇异积分交换子的有界性

本文在非齐次空间上给出了交换子[b,T](f)=bTf(x)-T(bf)(x)在b(x)是Lipschitz函数时的Lp(p＞1)有界性.     

三项指数和四次均值的精确计算公式(2)

本文进一步深入研究了三项指数和四次均值的计算问题.运用指数和的相关性质并结合求解同余方程组的方法与技巧,利用两种不同的方法获得了两个精确的均值计算公式,揭示了三项指数和的计算与同余方程组解的个数之间的本质联系,推广了已有的结果.     

关于TLS和LS解的扰动分析

1．引言本文采用卜］的记号．最小二乘（LS）和总体最小二乘（TLS）是科学计算中的两种重要方法．尤是TLS，近来已有多篇论文讨论［1－6，8－16］．奇异值分解（SVD）和CS分解是研究TLS和LS的重要工具．令ACm，BCm,C=(A,B)，A和C的SVD分别为（1．1）（1．2）其中P51为某个正整数，U，U，V，V均为西矩阵，UI，UI，VI，VI为上述矩阵的前P列，z1一山。g（。1，…，内），】2＝di。g（内十l，…，。小】1＝dl。g（61；…，站，】2二diag（4＋1；…，dk），。l三··2。120和dl三…三d。20分别为C和A的奇异值，Z＝mhfm．n十以…