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1.
Given a graph we are interested in studying the symmetric matrices associated to with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees. 相似文献
2.
Ya'akov Nahir 《International Journal of Mathematical Education in Science & Technology》2013,44(4):614-624
A procedure is presented by which the integration of a function such as cos n (x) or sin n (x) with n = 1, 2, 3, 4 … is facilitated. 相似文献
3.
带号图是每条边带有符号(正或负)的简单图.探讨了带号图的秩,刻画了秩为2与3的带号图,以及秩为4的带号二部图. 相似文献
4.
令$\eta(\Gamma)$和$c(\Gamma)$是符号图$\Gamma$的零度和基本圈数. 一个符号圈拼接图是指每个块都是圈的连通符号图. 本文证明了对任意符号拼接图$\eta(\Gamma)\le c(\Gamma)+1$成立, 并且刻画了等号成立的极图, 推广了王登银等人(2022)在简单圈拼接图上的结果. 此外, 我们证明了任意的符号拼接图$\eta(\Gamma)\neq c(\Gamma)$, 给出了满足$\eta(\Gamma)=c(\Gamma)-1$的符号拼接图的一些性质并刻画处$\eta(\Gamma)=c(\Gamma)-1$的二部符号拼接图. 相似文献
5.
AnEstimateofInequalityofSignatureandNullityforLinks¥LiQisheng(李起升)(Dept.OfMath.HenanUniversity,Kaifeng475001)Abstract:Aninequ... 相似文献
6.
Sang Youl Lee 《Proceedings of the American Mathematical Society》1999,127(11):3403-3412
We show that there exists a one-to-one correspondence between the class of certain block tridiagonal matrices with the entries or and the free monoid generated by generators and relation and give some applications for braids. In particular, we give new formulation of the reduced Alexander matrices for closed braids.
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Xiaobin Ma 《Linear and Multilinear Algebra》2013,61(11):2200-2211
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We obtain spectral properties of the Pascal graphs by exploring its spectral graph invariants such as the algebraic connectivity, the first three largest Laplacian eigenvalues and the nullity. Some open problems pertaining to the Pascal graphs are given. 相似文献
9.
林跃峰 《数学的实践与认识》2013,43(10)
研究次极大图(即链环分支数等于基圈数的连通平图)的唯一性.证明了无割点且包含子图K_4的连通平图G是次极大图当且仅当G同构于K_4,并刻画了包含子图K_4的次极大图的结构. 相似文献
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