完全图去除路P10的图谱特征
Spectral Characterization of the Complete Graph by Deleting P10
DOI: 10.12677/PM.2021.115107, PDF,   
作者: 林智浩：广东技术师范大学，数学与系统科学学院，广东 广州
关键词: 图谱；同谱图；谱特征；路；Graph Spectrum； Cospectral Graphs； Spectral Characterization； Path
摘要: 如果与图G同谱的所有图同构于图G，则称图G是由其图谱所决定的。设Kn\Pl是由完全图Kn去除图Pl的边所得到的子图，其中图Pl是长为l−1的路。Cámara和Haemers给出猜想1：对于任意的整数l(2≤l≤n)，Kn\Pl可由其邻接谱所决定。本文证明在l=10的情况下猜想1是正确的。
Abstract: A graph G is said to be determined by its spectrum if any graph having the same spectrum as G is isomorphic to G. Let Kn\Pl be the graph obtained from Kn by deleting edges of Pl, where Pl is a path of length l−1. Cámara and Haemers conjectured that Kn\Pl is determined by its adjacency spectrum for every (2≤l≤n). In this paper, we show that the conjecture is true for l=10.
文章引用：林智浩. 完全图去除路P10的图谱特征[J]. 理论数学, 2021, 11(5): 937-945. https://doi.org/10.12677/PM.2021.115107

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