图类αK_(α,α)UβCP(b)中的一类特殊整谱图

图G是一个简单,图G的补图记为G,如果G的谱完全由整数组成,就称G是整谱图,鸡尾酒会图CP (n)=K_(2n)-nK_2(K_(2n)是完全图)和完全二部图K_(a,a)都是整谱图.u_1表示图类αK_(α,α)UβCP(b)的一个主特征值,本文确图了当u_1=2b 1时,图类αK_(α,α)UβCP(b)中的所有的整谱图.     

Solid Solvates of C60 Compositions and Thermodynamics

Compositions of the solid solvates of C₆₀ with 1,2-dichlorobenzene and 1,3,5-trimethylbenzene were determined with the help of experimental procedures developed. Possible correlations between compositions and thermodynamic properties were discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

几何随机图大连通分支覆盖面积及其在传感器网络中的应用

随机网络中的大连通分支能体现一个网络的连通情况,是几何随机图研究的-个热点,具有重要的理论意义和应用价值.本文利用渗流理论,研究了几何随机图大连通分支覆盖面积所具有的性质,并将理论结果应用到大型无线传感器网络中,研究了无线传感器网络覆盖的性质.研究结果表明,对于节点服从泊松分布的大型无线传感器网络,其大连通分支覆盖区域大小与总区域大小的比值趋于-个常数,且并估计出了2维空间中没有被大连通分支所覆盖的连通区域(本文称为空洞)的大小.这些结果为衡量无线传感器网络性能提供了理论基础,对实际布网和网络优化等具有一定的指导意义.     

Effects of Ar/H/N‐ion bombardment on the surface free energy and friction behavior of the fullerene‐like hydrogenated carbon (FL‐C:H) film

The surface modification of the fullerene‐like hydrogenated carbon (FL‐C:H) film was achieved by bombardment using Ar, H, and N ions, respectively. A systematic comparison of X‐ray photoelectron spectroscopy (XPS) and Fourier transformation infrared(FTIR) spectra was made between the FL‐C:H film and ion‐bombarded films. The results show that ion bombardment resulted in the increase of sp³ C content, specially, new C? N bonds were formed for N‐ion‐bombarded film. The contact angle (CA) and friction coefficient of those films were measured. The surface free energy evaluated from the contact angle increased for ion‐bombarded films, and the most obvious increase was obtained for N‐ion‐bombarded film. The friction coefficient decreased for H‐ion‐bombarded film whereas it increased for N‐ion‐bombarded film, and the friction coefficient of Ar‐ion‐bombarded film was close to that of the FL‐C:H film. Copyright © 2008 John Wiley & Sons, Ltd.     

Expansion properties of random Cayley graphs and vertex transitive graphs via matrix martingales

The Alon–Roichman theorem states that for every ε> 0 there is a constant c(ε), such that the Cayley graph of a finite group G with respect to c(ε)log ∣G∣ elements of G, chosen independently and uniformly at random, has expected second largest eigenvalue less than ε. In particular, such a graph is an expander with high probability. Landau and Russell, and independently Loh and Schulman, improved the bounds of the theorem. Following Landau and Russell we give a new proof of the result, improving the bounds even further. When considered for a general group G, our bounds are in a sense best possible. We also give a generalization of the Alon–Roichman theorem to random coset graphs. Our proof uses a Hoeffding‐type result for operator valued random variables, which we believe can be of independent interest. © 2007 Wiley Periodicals, Inc. Random Struct. Alg., 2008     

Thermal decomposition of ammonium perchlorate based mixture with fullerenes

The effects of fullerenes, including fellerene soot (FS), extracted fullerene soot (EFS) and pure C₆₀ on the thermal decomposition of ammonium perchlorate (AP) compared with traditional carbon black (CB) catalyst has been studied by employing thermogravimetry (TG), differential thermal analysis (DTA), infrared spectroscopy (IR) and ignition temperature experiments. The results showed that the addition of CB and FS to AP reduced the activation energy as well as the temperature at maximum decomposition rate, but that of EFS and pure C₆₀ had little effect on the thermal decomposition of AP, and among all catalysts, FS was the best one.     

On the number of (r,r+1)‐ factors in an (r,r+1)‐factorization of a simple graph

For integers d≥0, s≥0, a (d, d+s)‐graph is a graph in which the degrees of all the vertices lie in the set {d, d+1, …, d+s}. For an integer r≥0, an (r, r+1)‐factor of a graph G is a spanning (r, r+1)‐subgraph of G. An (r, r+1)‐factorization of a graph G is the expression of G as the edge‐disjoint union of (r, r+1)‐factors. For integers r, s≥0, t≥1, let f(r, s, t) be the smallest integer such that, for each integer d≥f(r, s, t), each simple (d, d+s) ‐graph has an (r, r+1) ‐factorization with x (r, r+1) ‐factors for at least t different values of x. In this note we evaluate f(r, s, t). © 2009 Wiley Periodicals, Inc. J Graph Theory 60: 257‐268, 2009     

The Basis Number of Some Special Non-Planar Graphs

The basis number of a graph G was defined by Schmeichel to be the least integer h such that G has an h-fold basis for its cycle space. He proved that for m, n 5, the basis number b(K _m,n ) of the complete bipartite graph K _m,n is equal to 4 except for K _6,10, K _5,n and K _6,n with n = 5, 6, 7, 8. We determine the basis number of some particular non-planar graphs such as K _5,n and K _6,n , n = 5, 6, 7, 8, and r-cages for r = 5, 6, 7, 8, and the Robertson graph.     

Salem Numbers and Growth Series of Some Hyperbolic Graphs

Extending the analogous result of Cannon and Wagreich for the fundamental groups of surfaces, we show that, for the -regular graphs associated to regular tessellations of the hyperbolic plane by m-gons, the denominators of the growth series (which are rational and were computed by Floyd and Plotnick) are reciprocal Salem polynomials. As a consequence, the growth rates of these graphs are Salem numbers. We also prove that these denominators are essentially irreducible (they have a factor of X + 1 when m 2 mod 4; and when = 3 and m 4 mod 12, for instance, they have a factor of X ² – X + 1). We then derive some regularity properties for the coefficients f _n of the growth series: they satisfy K ⁿ – R < f _n < K ⁿ + R for some constants K, R < 0, < 1.     

A (2 + )-Approximation Scheme for Minimum Domination on Circle Graphs

The main result of this paper is a (2 + )-approximation scheme for the minimum dominating set problem on circle graphs. We first present an O(n²) time 8-approximation algorithm for this problem and then extend it to an time (2 + )-approximation scheme for this problem. Here n and m are the number of vertices and the number of edges of the circle graph. We then present simple modifications to this algorithm that yield (3 + )-approximation schemes for the minimum connected and the minimum total dominating set problems on circle graphs. Keil (1993, Discrete Appl. Math.42, 51–63) shows that these problems are NP-complete for circle graphs and leaves open the problem of devising approximation algorithms for them. These are the first O(1)-approximation algorithms for domination problems on circle graphs.