The girth of a 4-homogeneous bipartite graph

In this paper, it is proved that the girth of a 4-homogeneous bipartite graph with valency greater than 2 is at most 12.     

利用射影平面PG（2,Fq）中的一个二次曲线研究两类与三个类…

令Ｃ是Ｈ＝ＰＧ（２，Ｆｑ）中一个二次曲线，这里ｑ是一个偶素数的方幂，取一个二次曲线作为射影平面中的一个射影我们构作两个类和三个类的结合方案并计算它的参数。     

4-齐次二分图的围长

证明了度数大于2的4-齐次二分图的围长不超过12.     

利用射影平面中的二次曲线构作结合方案

设C是射影平面H=PG(2,Fq)中的一条二次曲线.把H看作射影空间PG(3,Fq)的无穷远超平面,那么H在PG(3,Fq)中的补空间是仿射空间X=AG(3,Fq).我们把H上的点集划分为2个或3个子集的并.设a≠b∈X.若线ab与H的交点属于第i个集合,定义a和b属于第i个结合类.我们证明上述构作是结合方案.最后,把H的某一点集作为处理集,构作出结合方案.     

利用射影空间中的埃尔米特簇构作结合方案

本文把N+1维射影空间看作一个N+1维仿射空间X和一个N维无穷远超平面H的并,利用埃尔米特簇把H上的点集划分为3个子集,对X中任两点a和b,如果线ab与H的交点属于第i个子集,定义a和b属于第i个结合类,我们证明上述构作是一个结合方案,并计算出其参数。     

对称群上交换图的完备码

设G是一个有限群,G上的交换图以G中非中心元素构成的集合为顶点集,其中两个不同的顶点x,y相邻当且仅当xy=yx.图的完备码问题是指:判断图是否具有完备码;如果图具有完备码,则如何找到该图的完备码.本文解决了对称群和交错群上交换图的完备码问题.     

AN ANZAHL THEOREM IN SINGULAR PSEUDO-SYMPLECTIC GEOMETRY OVER FINITE FIELDS

1 IntroductionLet F, be a fiuite field witl1 q elelllents. wl1ere q is a power of 2. We will follow tlie notationsand terntillologies in [11. LetThe singular pseudthsymplectic group with respect to Se,I over Fq denoted by PS=.+.+..=.+, (F,)is defiued to be tlie group fOrnled by all (2P + 6 + l) x (2v + b + l) nonsingUlar n1atrices T suchthat TSb.,T' == Sb,i. wl1ere TT denotes the transpose of T. If T 6 Ps=.+,+,.=.+, (Fq), then T isof the forlllwhere T1,S,T1,' = Se and T22 is nousin…     

利用伪辛空间中的迷向点集构作结合方案

令Ｆｑ是ｑ个元的有限域，其中ｑ是一个２的方幂。在本文我们假设δ＝１或２。     

GEOMETRIC CONSTRUCTION OF ASSOCIATION SCHEMES FROM NON-DEGENERATE QUADRICS

1. IntroductionThe geometry of quadrics in finite-dimensional projective spaces has been studiedby E.J.F. Primrose[1], D.K. Ray-ChaudhUxi[','] and I.M. Chakravarti[4]. In 1993, 1.M.Chakravartils] derived some association schemes from nondegenerate and degenerate Hermitian varieties. In [6], we constructed association schemes from the set of isotropic points inpseudthsymplectic spaces. In this paper) we will construct three-class association schemesfrom nolldegenerate quadrics.Let Fi be …     

GEOMETRIC CONSTRUCTION OF ASSOCIATIONSCHEMES FROM DEGENERATE QUADRICS INPROJECTIVE SPACES PG(2ν δ ι-1, Fq) FOR q ODD

1IntroductionThegeometryofquadricsandHerntitianvarietiesinfinite-dimensionalprojectivespaceshasbeenstudiedbyE-J.F.Primrose[6],D.K.tw-Chaudhuri['l8],I.M.Chakravarti["'],andR.C-BoseandI-M-Ch.kravarti[1].Inl993,I.M.Chak.ava,ti[4]derivedsomeassociationschemesandcodesfromuondegenerateHerndtia-nvarieties.In[1o],weconstructedsomedriiliesofassociationschemesfromthesetofisotropicpointsinpseudo-symplecticspaces.Inthispaper5weconsiderdegenerateqlledricsandconstructafamilyoffour-classassociations…