| 单圈图H(p,tK_{1,m})的Laplacian谱刻画 |
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| 引用本文： | 梅若星,王力工,王陆华,王展青.单圈图H(p,tK_{1,m})的Laplacian谱刻画[J].运筹学学报,2015,19(1):57-64. |
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| 作者姓名： | 梅若星 王力工 王陆华 王展青 |
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| 作者单位： | 1. 西北工业大学理学院应用数学系, 西安 710072; |
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| 基金项目： | 国家自然科学基金(No. 11171273), 国家级大学生创新创业训练计划项目(No. 201410699079) |
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| 摘 要： | 设图\,$H(p,tK_{1,m})$\,是一个顶点数为\,$p+mt$\,的连通单圈图，它是由圈\,$C_{p}$\,的依次相邻的\,$t(1\leq t\leq p)$\,个顶点、每一个顶点分别与星\,$K_{1,m}$\,的中心重合而得到的单圈图. 证明了单圈图\,$ H( p,p K_{1,4})$, $H(p,p K_{1,3})$, $H(p,(p-1)K_{1,3})$\,是由它们的\,Laplacian\,谱确定的，并证明了当\,$p$\,为偶数时，单圈图\,$H(p,$2K_{1,3})$, $H( p,(p-2) K_{1,3})$, $H(p,(p-3)K_{1,3})$\,也是由它们的\,Laplacian\,谱确定的.
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| 关 键 词： | Laplacian谱 邻接谱 单圈图 |
| 收稿时间： | 2014-07-18 |
Laplacian spectral characterizations of unicyclic graphs H( p,t K_{ 1, m}) |
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| MEI Ruoxing,WANG Ligong,WANG Luhua,WANG Zhanqing.Laplacian spectral characterizations of unicyclic graphs H( p,t K_{ 1, m})[J].OR Transactions,2015,19(1):57-64. |
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| Authors: | MEI Ruoxing WANG Ligong WANG Luhua WANG Zhanqing |
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| Institution: | 1. Department of Applied Mathemtics, School of Science, Northwestern Polytechnical University, Xi'an 710072, China |
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| Abstract: | Let $H(p,tK_{1,m})$ be a connected unicyclic graph with $p+mt$ vertices obtained from $C_{p}$ by attaching the center of star $K_{1,m}$ to each one of $t$ mutual adjacent vertices of the cycle $C_{p}$,respectively. In this paper, it is proved that the unicyclic graphs $H(p,p K_{1,4})$, $H(p,p K_{1,3})$, $H((p,(p-1) K_{1,3} )$ are determined by their Laplacian spectra, and when $ p $ is even number, the unicyclic graphs $H(p,2 K_{1,3})$, $H(p,(p-2)K_{1,3})$, $H(p,(p-3)K_{1,3})$ are also determined by their Laplacian spectra. |
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| Keywords: | Laplacian spectrum adjacency spectrum unicyclic graph |
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