最小化图的拉普拉斯行列式

IF 1 3区数学 Q2 MATHEMATICS

Journal of Graph Theory Pub Date : 2025-07-01 DOI:10.1002/jgt.23275

Nathan Albin, Joan Lind, Anna Melikyan, Pietro Poggi-Corradini

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引用次数: 0

摘要

本文研究了加权图拉普拉斯在简单非退化条件下的行列式的极值问题。给出了拉普拉斯式的行列式离零有界和权值最小集存在的充分必要条件。这些条件是根据随机生成树的性质和图上的一种密度给出的。这些结果推广和扩展了Melikyan的工作。

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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Minimizing the Determinant of the Graph Laplacian

In this paper, we study extremal values for the determinant of the weighted graph Laplacian under simple nondegeneracy conditions on the weights. We derive necessary and sufficient conditions for the determinant of the Laplacian to be bounded away from zero and for the existence of a minimizing set of weights. These conditions are given both in terms of properties of random spanning trees and in terms of a type of density on graphs. These results generalize and extend the work of Melikyan.

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来源期刊

Journal of Graph Theory 数学-数学

CiteScore

1.60

自引率

22.20%

发文量

130

审稿时长

6-12 weeks

期刊介绍： The Journal of Graph Theory is devoted to a variety of topics in graph theory, such as structural results about graphs, graph algorithms with theoretical emphasis, and discrete optimization on graphs. The scope of the journal also includes related areas in combinatorics and the interaction of graph theory with other mathematical sciences. A subscription to the Journal of Graph Theory includes a subscription to the Journal of Combinatorial Designs .