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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, PP. 937-945

Keywords: 图谱，同谱图，谱特征，路
Graph Spectrum, Cospectral Graphs, Spectral Characterization, Path

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Abstract:

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。
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.

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