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Spectral characterization of the complete graph removing a path: Completing the proof of Cámara–Haemers Conjecture
Discrete Mathematics ( IF 0.7 ) Pub Date : 2021-01-11 , DOI: 10.1016/j.disc.2020.112275
Muhuo Liu , Xiaofeng Gu

A graph G is ADS if every A-cospectral graph of G is isomorphic to G. Denote by KnPk the graph obtained from the complete graph Kn with n vertices by deleting all edges of a path Pk with k vertices. In 2014, Cámara and Haemers conjectured that KnPk is ADS for every 2kn. The conjecture has been confirmed for k=n (Doob and Haemers, 2002), 2k6 (Cámara and Haemers, 2014), 7k9 (Mao et al., 2019) and k20 (Liu et al., 2020). In this paper, we completely settle the conjecture by proving the remaining cases.



中文翻译:

完整图形的光谱表征消除了路径:完成Cámara–Haemers猜想的证明

G一种-d小号 如果每个 一种的-cospectral图 G 同构 G。表示为ķñPķ 从完整图获得的图 ķññ 通过删除路径的所有边来形成顶点 Pķķ顶点。2014年,Cámara和Haemers推测ķñPķ一种-d小号 每一个 2ķñ。该猜想已被确认ķ=ñ (Doob和Haemers,2002年), 2ķ6 (Cámaraand Haemers,2014), 7ķ9 (Mao et al。,2019)和 ķ20(Liu et al。,2020)。在本文中,我们通过证明剩余的情况来完全解决猜想。

更新日期:2021-01-12
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