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图G称为上连通的,若对每个最小割集C,G-C有孤立点,G称为超连通的,若对每个最小割集C,G-C恰有两个连通分支,且其中之一为弧立点,本文刻划了上连通和超连通三次点传递图。 相似文献
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《数学的实践与认识》2019,(22)
(d,r,κ)-析取矩阵是分组测试理论中的一个Inhibitor模型.利用两个已知的(d,r,k)-析取矩阵定义了它们的卡氏积,并计算了这个新(d,r,κ)-析取矩阵的参数. 相似文献
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鉴于R iem ann积分对区间的分割和取点的双重任意性要求给应用带来的困难,本文中我们将选择“等距分割”这种特殊的分割方式来定义函数的可积性,即所谓“等分可积”.从表面上看,等分可积性要弱于R iem ann可积性,但本文将证明这两种可积性是等价的.文中还给出了等分可积准则. 相似文献
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通过变量变换的方法,将文[1]中一类广义Riccati方程的三个充分性判据统一起来,并加以推广.充分利用参数λ,κ的可变性揭示该结果与现有Riccati方程可积性间的关系,扩大了Riccati方程的可积性范围. 相似文献
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在弱Hopf代数上,定义了交叉积概念,并且得到了它的两种特殊形式冲积和扭积.特别地,给出了扭积为弱Hopf代数的一个充要条件,推广了Hopf代数的相应结论. 相似文献
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On optimizing edge connectivity of product graphs 总被引:1,自引:0,他引:1
Jianping Ou 《Discrete Mathematics》2011,(6):172
This work studies the super edge connectivity and super restricted edge connectivity of direct product graphs, Cartesian product graphs, strong product graphs and lexicographic product graphs. As a result, sufficient conditions for optimizing the edge connectivity and restricted edge connectivity of these graphs are presented. 相似文献
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We generalize Brylawski’s formula of the Tutte polynomial of a tensor product of matroids to colored connected graphs, matroids,
and disconnected graphs. Unlike the non-colored tensor product where all edges have to be replaced by the same graph, our
colored generalization of the tensor product operation allows individual edge replacement. The colored Tutte polynomials we
compute exists by the results of Bollobás and Riordan. The proof depends on finding the correct generalization of the two
components of the pointed Tutte polynomial, first studied by Brylawski and Oxley, and on careful enumeration of the connected
components in a tensor product. Our results make the calculation of certain invariants of many composite networks easier,
provided that the invariants are obtained from the colored Tutte polynomials via substitution and the composite networks are
represented as tensor products of colored graphs. In particular, our method can be used to calculate (with relative ease)
the expected number of connected components after an accident hits a composite network in which some major links are identical
subnetworks in themselves.
相似文献
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充分利用图的字典积的结构证明了以下结论:如果图G_1的每连通分支都非平凡,图G_2的阶数大于3,那么它们的字典积G_1[G_2]具有非零3-流. 相似文献
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Let G be a connected graph with order n, minimum degree δ = δ(G) and edge-connectivity λ = λ(G). A graph G is maximally edge-connected if λ = δ, and super edge-connected if every minimum edgecut consists of edges incident with a vertex of minimum degree. Define the zeroth-order general Randi? index \(R_\alpha ^0\left( G \right) = \sum\limits_{x \in V\left( G \right)} {d_G^\alpha \left( x \right)} \), where dG(x) denotes the degree of the vertex x. In this paper, we present two sufficient conditions for graphs and triangle-free graphs to be super edge-connected in terms of the zeroth-order general Randi? index for ?1 ≤ α < 0, respectively. 相似文献
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An edge cut of a connected graph is called restricted if it separates this graph into components each having order at least
2; a graph G is super restricted edge connected if G−S contains an isolated edge for every minimum restricted edge cut S of G. It is proved in this paper that k-regular connected graph G is super restricted edge connected if k > |V(G)|/2+1. The lower bound on k is exemplified to be sharp to some extent. With this observation, we determined the number of edge cuts of size at most 2k−2 of these graphs.
Supported by NNSF of China (10271105); Ministry of Science and Technology of Fujian (2003J036); Education Ministry of Fujian
(JA03147) 相似文献
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Oleg Pikhurko 《Graphs and Combinatorics》2007,23(6):681-689
A graph G is product anti-magic if one can bijectively label its edges with integers 1, . . . ,e(G) so that no two vertices have the same product of incident labels. This property was introduced by Figueroa-Centeno, Ichishima,
and Muntaner-Batle who in particular conjectured that every connected graph with at least 4 vertices is product anti-magic.
Here, we completely describe all product anti-magic graphs of sufficiently large order, confirming the above conjecture in
this case. Our proof uses probabilistic methods.
Reverts to public domain 28 years from publication.
Partially supported by the National Science Foundation, Grant DMS-0457512. 相似文献
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