有向图的拉普拉斯特征值的k个最大绝对值之和

IF 0.7 4区 数学 Q2 Mathematics
Xiuwen Yang, Xiaogang Liu, Ligong Wang
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引用次数: 0

摘要

设$L(G)$为有向图$G$的拉普拉斯矩阵,$S_k(G)$为$G$的拉普拉斯特征值的$k$最大绝对值之和。设$C_n^+$为有向图,其顶点为$n+1$,由有向循环$C_n$通过附加一条尾在$C_n$上的垂弧得到。如果有向图不包含$C_{\ell}^+$作为任何$2\leq \ell \leq n-1$的子向图,则该有向图是$\mathbb{C}_n^+$自由的。本文给出了$n$阶有向图$S_n(G)$的下界。给出了有向环的$S_k(G)$和无单环有向图的$\mathbb{C}_n^+$的精确值。此外,我们还得到了具有顶点不相交有向环的$\mathbb{C}_n^+$自由有向图的$S_k(G)$的上界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the sum of the k largest absolute values of Laplacian eigenvalues of digraphs
Let $L(G)$ be the Laplacian matrix of a digraph $G$ and $S_k(G)$ be the sum of the $k$ largest absolute values of Laplacian eigenvalues of $G$. Let $C_n^+$ be a digraph with $n+1$ vertices obtained from the directed cycle $C_n$ by attaching a pendant arc whose tail is on $C_n$. A digraph is $\mathbb{C}_n^+$-free if it contains no $C_{\ell}^+$ as a subdigraph for any $2\leq \ell \leq n-1$. In this paper, we present lower bounds of $S_n(G)$ of digraphs of order $n$. We provide the exact values of $S_k(G)$ of directed cycles and $\mathbb{C}_n^+$-free unicyclic digraphs. Moreover, we obtain upper bounds of $S_k(G)$ of $\mathbb{C}_n^+$-free digraphs which have vertex-disjoint directed cycles.
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来源期刊
CiteScore
1.20
自引率
14.30%
发文量
45
审稿时长
6-12 weeks
期刊介绍: The journal is essentially unlimited by size. Therefore, we have no restrictions on length of articles. Articles are submitted electronically. Refereeing of articles is conventional and of high standards. Posting of articles is immediate following acceptance, processing and final production approval.
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