华东师范大学学报（自然科学版） >

2016 , Vol. 2016 >Issue 6: 139 - 144

DOI: https://doi.org/10.3969/j.issn.1000-5641.2016.06.015

数学

基于正则图的锥图的Q-谱确定性

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  • 上海理工大学 理学院, 上海 200093

收稿日期: 2015-10-23

  网络出版日期: 2017-01-13

基金资助

国家自然科学基金(11301340, 11201303); 上海市自然科学基金(12ZR1420300); 沪江基金(B14005)

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Q-spectral characterization of multicones over some regular graphs

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  • College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China

Received date: 2015-10-23

  Online published: 2017-01-13

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摘要

研究了锥图G ∨ Ks的 Q- 谱确定性, 其中 G 为 n 阶 r－正则图, Ks 为 s 阶完全图. 证明了, 对于任意正整数 s, 当 r=n-2 (n ≥ 4)时, G ∨ Ks 由其 Q- 谱确定; 当 r=n-3 (n ≥ 6)时, G ∨ Ks 由其 Q- 谱确定当且仅当 G 的补图 overline{G} 不含 三角形 C3.

关键词： 无符号拉普拉斯谱; Q- 谱; 锥图; 谱确定性

本文引用格式

吴宝丰, 庞琳琳 . 基于正则图的锥图的Q-谱确定性[J]. 华东师范大学学报（自然科学版）, 2016 , 2016(6) : 139 -144 . DOI: 10.3969/j.issn.1000-5641.2016.06.015

Abstract

The Q-spectral characterization of the multicone graph G ∨ Ks is investigated, where G is a r-regular graph of order n and Ks is a complete graph of order s. We prove that for any positive integer s, the multicone graph G ∨ Ks is determined by its Q-spectrum if r = n−2 and n ≥ 4. We also show that for any positive integer s, if r = n−3 and n ≥ 6, the multicone graph G ∨ Ks is determined by its Q-spectrum if and only if the complement of G has no triangles.

Key words： signless Laplacian spectrum; Q-spectrum; multicone graph; spectral characterization

参考文献

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