完全图的剖分图的线图的谱

如果一个图G的邻接矩阵A(G)的特征多项式的所有特征值全为整数,则称图G是整的.设图L2(Kp):L(s(Kp))是完全图Kp的剖分图S(Kp)的线图.在这篇文章里,我们利用图的理论给出了S(Kp)和L2(Kp)的特征多项式及其谱.对于图L2(Kp),得到了其补图、线图、线图的补图及补图的线图的特征多项式.也证明了这些图都是整图.这些整图的发现是对整图的研究的一个新贡献.     

特殊图b-色数的相关性质

图染色是图论中研究热点问题之一,在许多领域都有重要的应用.用χ(G)和φ(G)分别表示连通图G的色数和b-色数.对连通图R,S,称图G不含导出{R,S},如果图G不含同构于R和S的导出子图.本文证明了对任意连通的至少4个顶点的图R,S,连通(或者2-边连通或者2-连通)不含{R,S}的图G满足χ(G)=φ(G)当且仅当...     

交错群A_5的3度Cayley图

设G是一个有限群,S是群G的一个不含单位元1的子集,则G的关于S的Cayle图Γ=Cay(G,S)可由如下关系式定义:V(Γ)=GE(Γ)={(g,sg)|g∈G,s∈S}给出3度Cayley图Γ=Cay(As,S),即|S|=3时三个不同构类图的特征刻划,见定理1.     

二分图中含大圈的 2―因子(英文)

本文给出了均衡二分图有一个2-因子恰含 k 个大圈的度条件。设 G = (V1,V2;E) 是一个二分图,满足 |V1| = |V2| = n ≥ sk,其中 s ≥ 3 和 k ≥ 1 是两个整数。如果图 G 的最小度至少为 (1 ? 1/s)n + 1,那么 G 有一个2-因子恰含 k 个圈使得每个圈长至少为 2s。     

二分图中含大圈的2-因子

本文给出了均衡二分图有一个2-因子恰含k个大圈的度条件。设G=(V1,V2 E)是一个二分图,满足|V1|=|V2|=n≥sk。其中s≥3和k≥1是两个整数。如果图G的最小度至少为[(1-1／s)n] 1。那么G有一个2-因子恰含k个圈使得每个圈长至少为2s。     

图的2-距离控制数为[p/3]的必要条件

N.Sridharan等证明了阶数为p的2-距离控制数γ2(G)≤[p/3],并给出了p=3k(k=1,2,…)时,γ2(G)=p/3的充要条件.在这些结果的基础上,给出当p为任意正整数时,2γ(G)=[p/3]的一个必要条件:设G是阶数为p≥10的连通图,若2γ(G)=[p/3]且G A0,则G至少有一个悬挂点,这里A0是给定的图集.     

图变换及其在图的最小无符号拉普拉斯特征值的应用北大核心CSCD

假定G是一个带有点集V(G)={v_(1),v_(2),···,v_(n)}的连通简单图,图G的邻接矩阵A(G)=(a_(ij))_(n×n),其中点vi与点vj相邻,则a_(ij)=1;否则a_(ij)=0。我们定义度矩阵D(G)=diag(dG(v_(1)),dG(v_(2)),···,dG(v_(n))),其中dG(v_(i))是图G中点v_(i)(1≤i≤n)的度数。定义图G的无符号拉普拉斯矩阵Q(G)=D(G)+A(G),因为Q(G)是一个半正定矩阵,所以可将其特征值设为λ_(1)(G)≥λ_(2)(G)≥···≥λ_(n)(G)≥0,其中特征值λn(G)也称为图G的最小无符号拉普拉斯特征值。对补图的最小无符号拉普拉斯特征值问题进行了研究,报告了相关问题的研究现状,给出了两种图变换,并且应用他们去确定所有双圈图的补图中最小无符号拉普拉斯特征值取最小的唯一图。     

几类含圈图的全着色

对于图G=(V,E),一个正常全着色就是从V∪E到一个整数集的映射,使V∪E中的任意两个相邻或相关联的元素都着不同的颜色,图G=(V,E)的全色数xT(G)定义为xT(G)=min{k|存在G的一个正常k-全着急},本文对一类特殊图-含圈图的全着色给出了几个定理,验证了全着色猜想。     

图中具有分数(g,f)-因子的若干充分条件

设g和f分别是定义在图G的顶点集合V(G)上的整数值函数且对每个x∈V(G)有0≤g(x)≤f(x)。本文给出了一个图有分数(g,f)-因子的若干充分条件。     

哈密尔顿图和邻域并

邻域并条件是近十年来研究哈密尔顿图的得力工具之一。本文得到距离是2的点对的邻域并条件下的哈密尔顿图结果：若2连通n≥3阶图G距离是2的任意两点：x，y均有|N(x)∪N(y)|≥(2n-4)／3，则G是哈密尔顿图或G∈{G2：3K(n-2)／3，K(n-2)／3：K(n 1)／3：K(n 1)／3、Kn／3：Kn/3：Kn／3}。此结果改进一些已知结果。     

Two “Dual” Families of Nearly-Linear Codes over ℤ p , p odd

Since the paper by Hammons e.a. [1], various authors have shown an enormous interest in linear codes over the ring ℤ₄. A special weight function on ℤ₄ was introduced and by means of the so called Gray map ϕ : ℤ₄→ℤ₂ ² a relation was established between linear codes over ℤ₄ and certain interesting non-linear binary codes of even length. Here, we shall generalize these notions to codes over ℤ _p2 where p is an arbitrary prime. To this end, a new weight function will be proposed for ℤ _p2 . Further, properties of linear codes over ℤ _p2 will be discussed and the mapping ϕ will be generalized to an isometry between ℤ _p2 and ℤ _p ^p , resp. between ℤ _p2 ⁿ and ℤ _p ^pn . Some properties of Galois rings over ℤ _q will be described and two dual families of linear codes of length n = p ^m − 1, gcd(m, p) = 1, over ℤ _q will be constructed. Taking q = p ², their images under the new mapping can be viewed as a generalization of the binary Kerdock and the Preparata code, although they miss some of their nice combinatorial properties. Received: June 19, 2000; revised version: November 6, 2000     

Measurement of cosmogenic (32)p and (33)p activities in rainwater and seawater

We have developed a new method for the collection, purification, and measurement of natural levels of (32)P and (33)P in rain, marine particulates, and dissolved constituents of seawater. (32)P and (33)P activities were measured using a recently developed ultra-low-level liquid scintillation counter. Measurement by liquid scintillation counting allows, for the first time, simultaneous measurement of both (32)P and (33)P. Furthermore, (33)P activities are measured with high efficiency (>50%), regardless of the amount of stable phosphorus in the sample. Liquid scintillation also produces energy specific β spectra which has enabled us to identify previously unrecognized β-emitting contaminants in natural samples. In order to remove these contaminants, new methods of purification have been developed which utilize a series of precipitations and anion and cation exchange columns. Rainwater and dissolved seawater samples were extracted from large volumes of rain- and seawater, 5-20 and >5000 L, respectively, using iron-impregnated polypropylene filters. On these filters, it was possible to load between 25 and 30% Fe(OH)(3) by weight, over twice that loaded on previously utilized materials. Using our collection, purification, and liquid scintillation counting techniques, it was possible to obtain specific (32)P and (33)P activities with less than 10% error (2σ) in rainwater and 20% error (2σ) in seawater.     

Fast silicon p doped low temperature bolometer

The construction of a fast silicon p doped low temperature bolometer is described. It is a 5 × 5 × 0.3 mm Si <100 > n-type chip whose surface has been implanted with p doses of the order of 10¹⁸cm⁻³. The bolometer has a response time better than 1 μs, a responsivity of 10⁴VW⁻¹ and a NEP of .     

p型ZnO薄膜研究进展

ZnO薄膜是一种应用广泛的半导体材料.近几年来,随着对ZnO的光电性质及其在光电器件方面应用的开发研究,ZnO薄膜成为研究热点之一.制备掺杂的p型ZnO是形成同质p-n结以及实现其实际应用的重要途径.近来已在p型ZnO及其同质结发光二极管(LED s)研究方面取得了较大的进展.目前报道的p型ZnO薄膜的电阻率已降至10-3Ω.cm量级.得到了具有较好非线性伏安特性的ZnO同质p-n结和紫外发光LED.本文就其最新进展进行了综述.     

Improved p charts to monitor process quality

It is a common practice to monitor the fraction p of non-conforming units to detect whether the quality of a process improves or deteriorates. Users commonly assume that the number of non-conforming units in a subgroup is approximately normal, since large subgroup sizes are considered. If p is small this approximation might fail even for large subgroup sizes. If in addition, both upper and lower limits are used, the performance of the chart in terms of fast detection may be poor. This means that the chart might not quickly detect the presence of special causes. In this paper the performance of several charts for monitoring increases and decreases in p is analyzed based on their Run Length (RL) distribution. It is shown that replacing the lower control limit by a simple runs rule can result in an increase in the overall chart performance. The concept of RL unbiased performance is introduced. It is found that many commonly used p charts and other charts proposed in the literature have RL biased performance. For this reason new control limits that yield an exact (or nearly) RL unbiased chart are proposed.     

Electromagnetic confinement and shaping for plate-form p

The relationship between melt shape, electromagnetic pressure and magnetic field is studied for electromagnetic confinement and shaping of plate-form part. The results of experimental observation and theoretical inference can be summarized as follows. As the melt thickness a is large enough, causing the ratio of plate thickness to current theoretic skin depth a/delta larger than 2.2, the electromagnetic pressure acting on melt can be simply expressed as P-m = B-2/2 mu, and the melt shape would be known only by measuring the distribution of magnetic flux density As a is small and makes the ratio a/delta less than 2.2, the melt shape and electromagnetic pressure for confining and shaping are determined not only by magnetic flux density B but also by melt thickness a, electromagnetic parameter mu gamma and current frequency f. In this paper, an equation used to calculate electromagnetic pressure acting on "thin plate-form melt" is brought forward. The equation gives a precise relationship between electromagnetic pressure factor p and melt thickness a, electromagnetic parameter mu gamma and current frequency f.     

Computation of detour index of TUHC6[2p, q] nanotubes for any p and q

The detour d(i, j) between vertices i and j of a graph is the number of edges of the longest path connecting these vertices. The matrix whose (i, j)-entry is the detour between vertices i and j is called the detour matrix. The half sum D of detours between all pairs of vertices (in a connected graph) is the detour index, i.e., D = (1/2) Sigma(j) Sigma(i) d(i, j). In this paper, we computed the detour index of TUHC6[2p, q] nanotubes for any p and q.