Abstract A graph G is said to be A − D S if every graph having the same adjacency spectrum is isomorphic to G . Let K n ∖ P k be the graph obtained from the complete graph K n with n vertices by removing all edges of a path P k with k vertices. It was shown by Doob and Haemers that K n ∖ P n is A − D S . In 2014, Camara and Haemers conjectured that K n ∖ P k is A − D S for every 2 ≤ k ≤ n , and they succeeded in proving it for 2 ≤ k ≤ 6 . Recently, Mao, Cioabă and Wang verified the conjecture for 7 ≤ k ≤ 9 . In this paper, we show that the conjecture is true for all k ≥ 20 .

中文翻译：

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去除路径的完整图的光谱表征

摘要 如果每个具有相同邻接谱的图都与 G 同构，则称图 G 是 A - DS。令 K n ∖ P k 是通过删除具有 k 个顶点的路径 P k 的所有边而从具有 n 个顶点的完整图 K n 获得的图。Doob 和 Haemers 证明 K n ∖ P n 是 A − DS 。2014 年，Camara 和 Haemers 推测 K n ∖ P k 是 A − DS 对于每 2 ≤ k ≤ n ，他们成功地证明了 2 ≤ k ≤ 6 。最近，Mao、Cioabă 和 Wang 验证了 7 ≤ k ≤ 9 的猜想。在本文中，我们证明该猜想对于所有 k ≥ 20 都是正确的。