On almost self-complementary graphs

A graph is called almost self-complementary if it is isomorphic to one of its almost complements X^c-I, where X^c denotes the complement of X and I a perfect matching (1-factor) in X^c. Almost self-complementary circulant graphs were first studied by Dobson and Šajna [Almost self-complementary circulant graphs, Discrete Math. 278 (2004) 23-44]. In this paper we investigate some of the properties and constructions of general almost self-complementary graphs. In particular, we give necessary and sufficient conditions on the order of an almost self-complementary regular graph, and construct infinite families of almost self-complementary regular graphs, almost self-complementary vertex-transitive graphs, and non-cyclically almost self-complementary circulant graphs.     

Designer Self-Assembling Peptide Materials for Diverse Applications

Summary: Macromolecuar chemistry and polymer science have had an enormous impact in many areas of science, engineering, medicine and our daily life. It has not only changed our way of life forever, but also continuously to improve our living standard. Macromolecuar chemistry now also encompasses bioengineering, biomimetics, designer biological materials and nanobiotechnology. Here we summarize a few classes of short peptides that we discovered and invented with broad applications including 3D tissue cell culture, reparative and regenerative medicine, tissue engineering, slow drug release, stabilization of membrane proteins for develop nanobiotechnology and molecular devices. Molecular design using short peptides as new materials will play increasingly important role in biomedical research, nanobiotechnology, clinical science and medicine.     

自余弱弦图

研究了一类自余(sc)弱弦图,即广义的自余弱弦图,得到了一些自余弱弦图的下边界和上边界.讨论了自余弱弦图的识别问题,特别地给出了一种O(m2)时间算法,能推断自余图是弱弦的还是非弱弦的,进一步作者编目了自余弱弦图的至少17种异体.     

标定自补图的计数

标定自补图的计数问题是“组合计数”理论中的著名难题，至今毫无进展，本文通过构造出阶≤９的全部自补图，获得了阶数的４，５，８和９的标定自补图的数目分别是１２，７２，１１２１４０和４６２７２２４。     

Some constructions of two-associate class PBIB designs

Summary Two-associate class PBIB designs, having association schemes of GD orL ₂ types, are constructed by using patterned matrices and by methods of taking unions of sets of blocks.     

Equienergetic self-complementary graphs

In this paper equienergetic self-complementary graphs on p vertices for every p = 4k, k ⩾ 2 and p = 24t + 1, t ⩾ 3 are constructed.     

q元非线性2-重量码(n,2,ω_1,ω_2)的检错性能

通过定义δ(xi,yi)函数,把2元非线性2-重量码(n,2,ω1,ω2)的性质推广到q元非线性2-重量码(n,2,ω1,ω2)上,根据码的距离分布和对偶距离分布讨论了码C的不可检错概率.给出了码C不是最佳检错码的几个条件.     

关于G.L.Chia和C.K.Lim的一个问题

G.L.Chia 和 C.K.Lim 提出下列问题:“设 G 是完全超紧图.若 G 是自补完全超紧图,那么 G 是自补图吗?”本文回答了这个问题.     

Self-Complementary Balanced Codes and Quasi-Symmetric Designs

An upper bound for self-complementary balanced codes is presented in this paper. We give a characterization for self-complementary balanced codes meeting this upper bound. We show that the existence of certain quasi-symmetric designs implies the existence of such optimal self-complementary balanced codes.