Minimizing the least Laplacian eigenvalue of signed complete graphs

IF 4.3 3区材料科学 Q1 ENGINEERING, ELECTRICAL & ELECTRONIC ACS Applied Electronic Materials Pub Date : 2024-08-12 DOI:10.1016/j.amc.2024.129002

Dan Li, Minghui Yan, Jixiang Meng

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Abstract

A signed graph Σ is a graph whose edges yield the signs ±1. Let $K_{n}$ be the complete graph with n vertices and $Σ = (K_{n}, F^{-})$ be a signed complete graph, where F is a subgraph induced by the negative edges of Σ. The least Laplacian eigenvalue of Σ is the least eigenvalue of its Laplacian matrix. A unicyclic graph is a connected graph containing exactly one cycle. In this paper, we focus on the least Laplacian eigenvalue of $Σ = (K_{n}, F^{-})$ , where F is a unicyclic graph.

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最小化有符号完整图的最小拉普拉奇特征值

有符号图 Σ 是一个图，其边的符号为 ±1。设 Kn 是有 n 个顶点的完整图，Σ=(Kn,F-) 是一个有符号的完整图，其中 F 是由Σ 的负边引起的子图。Σ 的最小拉普拉斯特征值是其拉普拉斯矩阵的最小特征值。单循环图是指包含一个循环的连通图。本文重点研究 Σ=(Kn,F-) 的最小拉普拉奇特征值，其中 F 是单环图。

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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