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1.
线有向图的幂敛指数   总被引:3,自引:0,他引:3  
设G是有向图,LG表示c的线有向图,本文得到了它们的幂敛指数及周期之间的关系:k(G)-1≤(LG)≤k(G)+1,p(LG)=p(G)特别地,当G为本原图时有:k(LG)=k(G)+1  相似文献
2.
公路定线的有向图模型   总被引:3,自引:0,他引:3  
杨元梁 《运筹与管理》2001,10(2):130-134
本给出一个公路定线的有向图模型,为公路定线问题提供一种较为系统的方法。  相似文献
3.
线有向图的幂敛指数   总被引:2,自引:1,他引:1       下载免费PDF全文
采用有向图的矩阵表示,得到了线有向图的幂敛指数和周期的有关结果.  相似文献
4.
n重线有向图的超连通性   总被引:1,自引:0,他引:1  
本文证明了,在最小度至少为3的前提下超弧连通有向图的迭代线图是超点连通的.作为推论,我们得到了Kautz网络和de Bruijn网络的超点连通性和超弧连通性.  相似文献
5.
Limit points of eigenvalues of (di)graphs   总被引:1,自引:0,他引:1  
The study on limit points of eigenvalues of undirected graphs was initiated by A. J. Hoffman in 1972. Now we extend the study to digraphs. We prove 1. Every real number is a limit point of eigenvalues of graphs. Every complex number is a limit point of eigenvalues of digraphs. 2. For a digraph D, the set of limit points of eigenvalues of iterated subdivision digraphs of D is the unit circle in the complex plane if and only if D has a directed cycle. 3. Every limit point of eigenvalues of a set D of digraphs (graphs) is a limit point of eigenvalues of a set of bipartite digraphs (graphs), where consists of the double covers of the members in D. 4. Every limit point of eigenvalues of a set D of digraphs is a limit point of eigenvalues of line digraphs of the digraphs in D. 5. If M is a limit point of the largest eigenvalues of graphs, then −M is a limit point of the smallest eigenvalues of graphs.  相似文献
6.
We show that the independent spanning tree conjecture on digraphs is true if we restrict ourselves to line digraphs. Also, we construct independent spanning trees with small depths in iterated line digraphs. From the results, we can obtain independent spanning trees with small depths in de Bruijn and Kautz digraphs that improve the previously known upper bounds on the depths.  相似文献
7.
For a digraph D, let L(D) and S(D) denote its line digraph and subdivision digraph, respectively. The motivation of this paper is to solve the digraph equation L(S(D))=S(L(D)). We show that L(S(D)) and S(L(D)) are cospectral if and only if D and L(D) have the same number of arcs. Further, we characterize the situation that L(S(D)) and S(L(D)) are isomorphic. Our approach introduces the new notion, the proper image D* of a digraph D, and a new type of connectedness for digraphs. The concept D* plays an important role in the main result of this paper. It is also useful in other aspects of the study of line digraphs. For example, L(D) is connected if and only if D* is connected; L(D) is functional (contrafunctional) if and only if D* is functional (contrafunctional). Some related results are also presented.  相似文献
8.
We show that the adjacency matrix M of the line digraph of a d-regular digraph D on n vertices can be written as M=AB, where the matrix A is the Kronecker product of the all-ones matrix of dimension d with the identity matrix of dimension n and the matrix B is the direct sum of the adjacency matrices of the factors in a dicycle factorization of D.  相似文献
9.
林秋英 《数学研究》2002,35(2):194-199
给出了一类特殊的广义deBruijn有向图的支撑树与欧环游的数目的简洁表示式,并得到了广义deBruijn有向叠线图的支撑树与欧拉环境数目的计算公式。  相似文献
10.
设D为有向图,T(D)为D的全有向图(Total-digraph),k(D)和p(D)分别为D的幂敛指数(Index of convergence)与周期(Period),本文证明了。1,对任意非平凡有向图D,p(T(D))=1,k(T(D))≤max{2p(D)-1,2K(D) 1},特别地,当D为本原有向图时,k(T(D))≤k(D) 1,当D不含有向圈时,k(T(D))=2k(D)-1;当D为有向圈Cn时,k(T(D))=2n-1.2。对任意非平凡强连通图D,k(T(D))≥Diam(D) 1。我们还证明了以上界是不可改进的最好界。  相似文献
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