具有任意大间隙集的阈值图

IF 1 3区数学 Q1 MATHEMATICS

Bulletin of the Malaysian Mathematical Sciences Society Pub Date : 2024-04-08 DOI:10.1007/s40840-024-01680-w

Abdullah Alazemi, Milica Anđelić, Haneen Zaidan

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引用次数: 0

摘要

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。

Threshold Graphs with an Arbitrary Large Gap Set

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Threshold Graphs with an Arbitrary Large Gap Set

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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来源期刊

Bulletin of the Malaysian Mathematical Sciences Society 数学-数学

CiteScore

2.40

自引率

8.30%

发文量

176

审稿时长

3 months

期刊介绍： This journal publishes original research articles and expository survey articles in all branches of mathematics. Recent issues have included articles on such topics as Spectral synthesis for the operator space projective tensor product of C*-algebras; Topological structures on LA-semigroups; Implicit iteration methods for variational inequalities in Banach spaces; and The Quarter-Sweep Geometric Mean method for solving second kind linear fredholm integral equations.