完全图拉普拉斯比率的研究
Laplacian Ratios of the Complete Graphs
DOI: 10.12677/PM.2024.144132, PDF, 下载: 134  浏览: 227  科研立项经费支持
作者: 董香帅：青海民族大学数学与统计学院，青海 西宁
关键词: 完全图；拉普拉斯矩阵；积和式；拉普拉斯比率；Complete Graphs； Laplacian Matrix； Permanent； Laplacian Ratio
摘要: Brualdi等人给出了图的拉普拉斯比率 π(G) 的定义，即树 G 的拉普拉斯矩阵积和式与其所有顶点 度的乘积。 Brualdi 和 Goldwasser 系统地研究了树的拉普拉斯比率的性质。 这篇文章是对完全 图删除 1-3 条边的拉普拉斯比率的研究。
Abstract: Laplacian ratios of graphs were first considered by Brualdi et al. The Laplacian ratio of π(G) is the permanent of the Laplacian matrix of G divided by the product of degrees of all vertices. Brualdi and Goldwasser studied systematicly the properties of Laplacian ratios of graphs. In this paper, we investigate the Laplacian ratios of all graphs obtained from complete graphs with 1-3 edges deleted.
文章引用：董香帅. 完全图拉普拉斯比率的研究[J]. 理论数学, 2024, 14(4): 250-261. https://doi.org/10.12677/PM.2024.144132

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