Which multicone graphs K_n?K_m are determined by their signless Laplacian spectrum? (The proof of a conjecture)

Ali Zeydi Abdian; Sara Pouyandeh; Bahman Askari

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Which multicone graphs K_n?K_m are determined by their signless Laplacian spectrum? (The proof of a conjecture)

机译：哪个多级图形k_n？k_m由其无靶拉瓦普拉斯谱决定？（猜想的证明）

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摘要

A multicone graph is defined to be the join of a clique and a regular graph. Let K_m and K_n denote a complete graph on m vertices and the complement of a complete graph on n vertices, respectively. In [X. Liu and P. Lu, Signless Laplacian spectral characterization of some joins, Electron. J. Linear Algebra 30.1 (2015)], it have been conjectured that the multicone graphs K_n ?K_m are determined by their signless Laplacian spectrum. In this short note, we prove this conjecture for n ≠ 3.

机译：多个图形被定义为Clique和常规图形的连接。设k_m和k_n分别表示m顶点上的完整图，分别在n顶点上的完整图的补充。在[X. 刘和P. Lu，一些加入，电子的无数拉普拉斯光谱表征。 J.线性代数30.1（2015）]，已经猜测了多级图K_N？K_M由其无特征拉普拉斯谱决定。在这个简短的注意事项中，我们证明了这个猜想n≠3。

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来源
《Journal of Discrete Mathematical Sciences and Cryptography》 |2019年第1期|共9页
作者
Ali Zeydi Abdian; Sara Pouyandeh; Bahman Askari;
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作者单位

Department of the Mathematical Science Lorestan University College of Science Lorestan Khoramabad Iran;

Department of Mathematics Payame Noor University P.O. Box 19395-3697 Tehran Iran;

Department of Mathematics Qorveh Branch Islamic Azad University Qorveh Iran;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
DS graph; Multicone graph; Signless Laplacian spectrum;

机译：DS图;多功能图;有偶数拉普拉斯谱;

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1. Which multicone graphs K_n?K_m are determined by their signless Laplacian spectrum? (The proof of a conjecture) [J] . Ali Zeydi Abdian, Sara Pouyandeh, Bahman Askari Journal of Discrete Mathematical Sciences and Cryptography . 2019,第1期

机译：哪个多级图形k_n？k_m由其无靶拉瓦普拉斯谱决定？（猜想的证明）
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Which multicone graphs K_n?K_m are determined by their signless Laplacian spectrum? (The proof of a conjecture)

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