具有完全两个不同主特征值的符号图的进一步结果

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-08-05 DOI:10.1016/j.disc.2025.114712

Zenan Du , Lihua You , Hechao Liu

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引用次数: 0

摘要

一个n阶的有符号图S的特征值λ，如果它的特征空间不正交于全一向量1，则它是一个主特征值。具有k（1≤k≤n）个不同主特征值的符号图的刻画是代数图论中已经研究的一个问题。在2020年，Z. staniki证明了一个签名图只有一个主特征值当且仅当它是净正则的。Du等人在2024年研究了恰好有两个不同主特征值的签名图，并将其分为四种情况。他们解决了两个案子，剩下的两个还没有解决。在本文中，我们完全解决了剩下的两种情况中的一种，从而解决了Du et al.(2024)[10]中的问题5.1。

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Further results on signed graphs with exactly two distinct main eigenvalues

An eigenvalue λ of a signed graph S of order n is a main eigenvalue if its eigenspace is not orthogonal to the all-ones vector 1. Characterizing signed graphs with exactly k

(1 \leq k \leq n)

distinct main eigenvalues is a problem in algebraic graph theory that has been studied. In 2020, Z. Stanić proved that a signed graph has exactly one main eigenvalue if and only if it is net-regular. Du et al. studied signed graphs with exactly two distinct main eigenvalues in 2024 and classified them into four cases. They solved two cases and left the other two as open problems. In this paper, we completely solve one of the remaining two cases, thus solving Problem 5.1 in Du et al. (2024) [10].

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.