Threshold Graphs with an Arbitrary Large Gap Set

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-04-08 DOI:10.1007/s40840-024-01680-w

Abdullah Alazemi, Milica Anđelić, Haneen Zaidan

引用次数: 0

Abstract

An interval in which a given graph has no eigenvalues is called a gap interval. We show that for any real number R greater than \(\frac{1}{2}(-1+\sqrt{2})\), there exist infinitely many threshold graphs with gap interval (0, R). We provide a new recurrence relation for computing the characteristic polynomial of the threshold graphs and based on it, we conclude that the sequence of the least positive (resp. largest negative) eigenvalues of a certain sequence of threshold graphs is convergent. In some particular cases, we compute the limit points.

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具有任意大间隙集的阈值图

一个给定图形没有特征值的区间被称为间隙区间。我们证明，对于大于 \(\frac{1}{2}(-1+\sqrt{2})\)的任意实数 R，存在无限多个间隙区间为（0，R）的阈值图。我们为计算阈值图的特征多项式提供了一种新的递推关系，并基于这种关系得出结论：某个阈值图序列的最小正（或最大负）特征值序列是收敛的。在某些特殊情况下，我们会计算极限点。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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