图的支配划分与最小团的关系

本文用色函数讨论了图Ｇ的团图Ｋ（Ｇ）为奇圈时ｃ（Ｇ）≤ｄ（Ｇ）成立的一个充分条件和Ｋ（Ｇ）为简单连通图时ｃ（Ｇ）≤ｄ（Ｇ）成立的一个充分条件．     

More on convexity numbers of closed sets in

The convexity number of a set is the least size of a family of convex sets with . is countably convex if its convexity number is countable. Otherwise is uncountably convex.

Uncountably convex closed sets in have been studied recently by Geschke, Kubis, Kojman and Schipperus. Their line of research is continued in the present article. We show that for all , it is consistent that there is an uncountably convex closed set whose convexity number is strictly smaller than all convexity numbers of uncountably convex subsets of .

Moreover, we construct a closed set whose convexity number is and that has no uncountable -clique for any 1$">. Here is a -clique if the convex hull of no -element subset of is included in . Our example shows that the main result of the above-named authors, a closed set either has a perfect -clique or the convexity number of is in some forcing extension of the universe, cannot be extended to higher dimensions.

     

Subinverses of fuzzy matrices

A matrix operation is examined for fuzzy matrices and interesting properties of fuzzy matrices are obtained using the operation. Particularly some properties concerning subinverses and regularity of fuzzy matrices are given and the largest subinverse is shown by the properties. The properties are closely related to inverses of fuzzy matrices and fuzzy equations. Moreover fuzzy preorders are examined using the matrix operation and basic properties are obtained. The results are considered to be useful for the theory of fuzzy matrices.     

联合能耗与负载均衡的虚拟网络映射方法

为解决弹性光网络中虚拟网络映射时能耗严重、资源分配不均的问题,该文提出一种联合能耗与负载均衡的虚拟网络映射（PC-LB-VONE）方法.在虚拟节点映射时,选择相邻链路长度短、光节点计算资源多与相邻链路带宽资源多的光节点映射.在虚拟链路映射时,提出一种基于极大团的候选光路资源匹配度单路径映射策略.当单路径映射失败时,设计基于链路负载均值的多路径映射策略.仿真结果表明,所提方法能在减少弹性光网络能耗的同时均衡网络负载.     

There exists no (15,5,4) RBIBD†*

An (n, M, d)_q code is a q‐ary code of length n, cardinality M, and minimum distance d. We show that there exists no (15,5,4) resolvable balanced incomplete block design (RBIBD) by showing that there exists no (equidistant) (14,15,10)₃ code. This is accomplished by an exhaustive computer search using an orderly algorithm combined with a maximum clique algorithm. © 2001 John Wiley & Sons, Inc. J Combin Designs 9: 357–362, 2001     

n圈中辐图的团覆盖数和团划分数

本文主要讨论 Petersen图的一类推广图—— n圈中辐图的团覆盖数和团划分数 ,由此得出该图的团覆盖数和团划分数相等的结论 ,同时给出了其在不同情况下的计算公式 .     

The maximum clique and the signless Laplacian eigenvalues

Lower and upper bounds are obtained for the clique number ω(G) and the independence number α(G), in terms of the eigenvalues of the signless Laplacian matrix of a graph G. This work was supported by the National Natural Science Foundation of China (No. 10771080), SRFDP of China (No. 20070574006) and by the Foundation to the Educational Committee of Fujian (No. JB07020).     

P4-free图的控制团及应用

得到了P4-free图的控制团的阶数为1或2,并利用此性质证明了P4-free图的线图是哈密顿的.     

Automorphisms and Distinguishing Numbers of Geometric Cliques

A geometric automorphism is an automorphism of a geometric graph that preserves crossings and noncrossings of edges. We prove two theorems constraining the action of a geometric automorphism on the boundary of the convex hull of a geometric clique. First, any geometric automorphism that fixes the boundary of the convex hull fixes the entire clique. Second, if the boundary of the convex hull contains at least four vertices, then it is invariant under every geometric automorphism. We use these results, and the theory of determining sets, to prove that every geometric n-clique in which n≥7 and the boundary of the convex hull contains at least four vertices is 2-distinguishable.