Spectral Slater index of tournaments

IF 0.7 4区 数学 Q2 Mathematics Electronic Journal of Linear Algebra Pub Date : 2022-02-22 DOI:10.13001/ela.2022.6407
A. Boussaïri, A. Chaïchaâ, B. Chergui, Sara Ezzahir, S. Lakhlifi, Soukaïna Mahzoum
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引用次数: 0

Abstract

The Slater index $i(T)$ of a tournament $T$ is the minimum number of arcs that must be reversed to make $T$ transitive. In this paper, we define a parameter $\Lambda(T)$ from the spectrum of the skew-adjacency matrix of $T$, called the spectral Slater index. This parameter is a measure of remoteness between the spectrum of $T$ and that of a transitive tournament. We show that $\Lambda(T)\leq8\, i(T)$ and we characterize the tournaments with maximal spectral Slater index. As an application, an improved lower bound on the Slater index of doubly regular tournaments is given.
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光谱斯莱特锦标赛指数
比赛的斯莱特指数$i(T)$$T$是为了使$T$可传递而必须反转的最小弧线数。本文从$T$的斜邻接矩阵的谱中定义了一个参数$\Lambda(T)$,称为谱Slater索引。该参数是对$T$的频谱和传递锦标赛的频谱之间的距离的度量。我们证明了$\Lambda(T)\leq8\, i(T)$,我们用最大的光谱Slater指数来描述锦标赛。作为应用,给出了双规则比赛的Slater指标的改进下界。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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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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