END-正则的循环图

称图X是End-正则图如果它的自同态幺半解EndX是正则的幺半解，即关于任意自同态f存在一个自同态g使得fgf=f。本文对顶点度数小于4的End-正则循环图进行了刻划。     

树的联的end-正则性

明确给出了具有正则自同态幺半群的两个树的联．     

图的完全正则自同态

作为图的代数分析的一部分，对图的自同态幺半群的研究近年来有一定的进展（参见［３］及［４］）。这类研究的主要目的在于将半群理论应用于图论。文献［５］研究了图的正则自同态及其逆。在此基础上本文进一步描述了图的完全正则自同态的组合特征；同时对含有完全正则自同态ｆ的极大子群，文中也明确给出了其单位元素及ｆ的逆     

具有完全正则自同态半群的分裂图

本文给出了具有完全正则自同态半群的分裂图的结构特征．其证明方法有望应用于其他图族自同态半群的正则性及完全正则性的研究．     

图的P-正则自同态幺半群

刻划了具有Ｐ－正则自同态幺半群的二分图,讨论了字典序积图的自同态幺半群的Ｐ－正则性。     

图的强化缩核与图的强自同态幺半群的正则性

本文研究图及其强自同态幺半群，首先刻画了图的强自同态幺半群的正则元，然后给出了此幺半群正则的充要条件，这推广了（１）和（２）中关于有限图的强自同态幺半群正则的结果。     

一族具有正则幺半群的图

本文给出了一族具有正则自同态幺半群的图及相应的自同态计数公式。     

分裂图的自同态幺半群的正则性

对自同态么半群正则的分裂图进行了刻划,从而关于分裂图回答了Ｋｎａｕｅｒ提出的一个公开问题［１］。     

距离正则图的推广

本文研究了直径为d(Γ) ≥ 2的距离正则图Γ的补图.利用Γ的交叉数分别证明了当d=2时,Γ的补图式强正则;当d ≥ 3时,Γ的补图是广义强正则.将文献[2]中的距离正则图Grassmann图、对偶极图、Hamming图推广到它们的补图,从而得到广义强正则图.     

一族具有正则绐幺半群的图

本文给出了一族具有正则自同态么半群的图及相应的自同态计数公式．     

The join of split graphs whose half-strong endomorphisms form a monoid

In this paper, the half-strong endomorphisms of the join of split graphs are investigated. We give the conditions under which the half-strong endomorphisms of the join of split graphs form a monoid.     

Endomorphism Spectra of Bipartite Graphs with Diameter Three and Girth Six

There are different endomorphisms for a graph. For a more systematic treatment of these endomorphisms the endomorphism spectrum and the endomorphism type of a graph are defined. Knauer characterized trees using their endomorphism types. The endomorphism type of bipartite graphs with diameter three and girth six is given in this paper.AMS Subject Classification (1991): 05C25 20M20Supported by the National Natural Science Foundation of China (19901012)     

On Distance-Regular Graphs with Height Two

Let be a distance-regular graph with diameter at least three and height h = 2, where . Suppose that for every in and in _d(), the induced subgraph on _d() ₂() is a clique. Then is isomorphic to the Johnson graph J(8, 3).     

用超广义线图构造整谱图

线图在图的谱理论研究中起着重要的作用.在本文中,通过研究超广义线图成为整谱图的充分条件,获得了一种全新的构造新的整 谱图的方法,运用这种方法,可以构造出无穷多个新的整谱图.     

广义彼得森图的2—可扩性

本文证明了当k≥3,n≠2k,3k时,广义彼得森图GP(n,k)中的任意两条不邻接边都包含在GP(n,k)的1-因子中。     

Regularity and Unit-regularity of Generalized Semigroups of Linear Transformations

Let V and W be vector spaces over a division ring D and L_D (V, W) the set of all linear transformations from V into W. For L_D(W, V), let (L_D (V, W), ) denote the semigroup L_D (V, W) with the operation * defined by * = for all , L_D(V, W). By a unit-regular semigroup we mean a semigroup S with identity having the property that for each a S, a = aua for some unit u S. The main purpose of this paper is to prove the following statements. The semigroup (L_D(V, W), ) is regular if and only if V = {0}, W = {0} or is an isomorphism from W onto V. The semigroup (L_D (V, W), ) is unit-regular if and only if (i) V = {0}, (ii) W = {0} or (iii) is an isomorphism from W onto V and dim_D V .     

Classification of Regular Planar Graphs with Diameter Two

In the present paper, the regular planar graphs with diameter two are classified.     

On a Decomposition of Complete Graphs

It is shown, among other results, that for any prime power q, the complete graph on 1+q+q ²+q ³ vertices can be decomposed into a union of 1+q Siamese Strongly Regular Graphs S R G(1+q+q ²+q ³,q+q ²,q–1,q+1) sharing 1+q ² cliques of size 1+q. Acknowledgments.The authors are indebted to a referee for a very extensive report and for many suggestions which improved the presentation of the paper tremendously.AMS Subject Numbers: 05B05, 05B20, 05E30This work was completed while the first author was on sabbatical leave visiting Institute for studies in theoretical Physics and Mathematics, (IPM), in Tehran, Iran. Support and hospitality is appreciated. Supported by an NSERC operating grant.