特征标次数图是一种连通图的单群

对有限单群G,假设其不可约特征标次数图Δ(G)连通,且图顶点集ρ(G)=π_1∪π_2∪{p},其中|π_1|,|π_2|≥1,π_1∩π_2=θ,且π_1与π_2中顶点不相邻.证明了Δ(G)满足上面的假设的有限单群G只有4种:M_(11),J_1,PSL_3(4)或²B_2(q2B_2(q²),其中q2),其中q²一1是Mersenne素数.     

Graphs with at most one signless Laplacian eigenvalue exceeding three

We determine all connected graphs with at most one signless Laplacian eigenvalue exceeding three.     

On perfectly two-edge connected graphs

This paper studies the graphs for which the 2-edge connected spanning subgraph polytope is completely described by the trivial inequalities and the so-called cut inequalities. These graphs are called perfectly 2-edge connected. The class of perfectly 2-edge connected graphs contains for instance the class of series-parallel graphs. We introduce a new class of perfectly 2-edge connected graphs. We discuss some structural properties of graphs which are (minimally with respect to some reduction operations) nonperfectly 2-edge connected. Using this we give sufficient conditions for a graph to be perfectly 2-edge connected.     

图论在网络出版传播中的应用

利用图论理论研究了网络连通度与广播时间的关系问题 ,获得了网络单信息广播时间的一个界和最少时间广播网的几个充分条件 ,并建立了一个有效的广播方案 .     

A vertex incremental approach for maintaining chordality

For a chordal graph G=(V,E), we study the problem of whether a new vertex u∉V and a given set of edges between u and vertices in V can be added to G so that the resulting graph remains chordal. We show how to resolve this efficiently, and at the same time, if the answer is no, specify a maximal subset of the proposed edges that can be added along with u, or conversely, a minimal set of extra edges that can be added in addition to the given set, so that the resulting graph is chordal. In order to do this, we give a new characterization of chordal graphs and, for each potential new edge uv, a characterization of the set of edges incident to u that also must be added to G along with uv. We propose a data structure that can compute and add each such set in O(n) time. Based on these results, we present an algorithm that computes both a minimal triangulation and a maximal chordal subgraph of an arbitrary input graph in O(nm) time, using a totally new vertex incremental approach. In contrast to previous algorithms, our process is on-line in that each new vertex is added without reconsidering any choice made at previous steps, and without requiring any knowledge of the vertices that might be added subsequently.     

子图识别的层分解方法

子图识别问题(SRP)就是在一个图G中确定并寻找是否存在和另一个图H相同构的子图．本文将引入图的层分解概念，并以此为基础建立识别图的同构子图的算法．该算法的复杂性为O(n(△-1)^k-1)，其中△是图G的度，即G中点的最大度，n，k分别是图G，H的阶．     

On some kinds of fuzzy connected spaces

In this paper we introduce new results in fuzzy connected spaces. Among the results obtained we can mention the good extension of local connectedness. Also we prove that in a T ₁-fuzzy compact space the notions c-zero dimensional, strong c-zero dimensional and totally c_i-disconnected are equivalent.     

On the Maximum Number of Cliques in a Graph

A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m edges; (2) graphs with n vertices, m edges, and maximum degree Δ; (3) d-degenerate graphs with n vertices and m edges; (4) planar graphs with n vertices and m edges; and (5) graphs with n vertices and no K₅-minor or no K_3,3-minor. For example, the maximum number of cliques in a planar graph with n vertices is 8(n − 2). Research supported by a Marie Curie Fellowship of the European Community under contract 023865, and by the projects MCYT-FEDER BFM2003-00368 and Gen. Cat 2001SGR00224.     

泛连通图的Faudree-Schelp定理和哈密尔顿连通图的Ore定理的注记

In this note more short proofs are given for Faudree-Schelp theorem and Ore theorem.