加权有符号图的拉普拉斯矩阵的不等式

IF 1 Q2 MATHEMATICS

Special Matrices Pub Date : 2019-01-01 DOI:10.1515/spma-2019-0026

K. H. Monfared, G. MacGillivray, D. Olesky, P. van den Driessche

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引用次数: 0

摘要

摘要我们研究了加权有符号图的拉普拉斯矩阵所得到的惯性集。首先，我们用一个独特的拉普拉斯惯性来刻画有符号图。然后我们证明了任何连通加权有符号图的边上的非零权有一个足够小的扰动，使得它的拉普拉斯矩阵的所有特征值都是简单的。接下来，我们给出了具有固定柔性τ（有符号图的组合参数）的有符号图可能的拉普拉斯惯性数的上界，并证明了这些上界对于无限族有符号图是尖锐的。最后，我们给出了有符号图的可能拉普拉斯不等式的顶点数的上界。

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Inertias of Laplacian matrices of weighted signed graphs

Abstract We study the sets of inertias achieved by Laplacian matrices of weighted signed graphs. First we characterize signed graphs with a unique Laplacian inertia. Then we show that there is a sufficiently small perturbation of the nonzero weights on the edges of any connected weighted signed graph so that all eigenvalues of its Laplacian matrix are simple. Next, we give upper bounds on the number of possible Laplacian inertias for signed graphs with a fixed flexibility τ (a combinatorial parameter of signed graphs), and show that these bounds are sharp for an infinite family of signed graphs. Finally, we provide upper bounds for the number of possible Laplacian inertias of signed graphs in terms of the number of vertices.

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.