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高校应用数学学报
高校应用数学学报  2016, Vol. 31 Issue (1): 73-82    
    
两类双圈图的Laplacian谱确定问题
王展青, 王力工*, 梅若星, 翟若男, 董占鹏
西北工业大学 理学院应用数学系, 陕西西安 710072
Two kinds of bicyclic graphs are determined by their Laplacian spectra
WANG Zhan-qing, WANG Li-gong, MEI Ruo-xing, ZHAI Ruo-nan, DONG Zhan-peng
Department of Applied Mathematics, School of Science, Northwestern Polytechnical University, Xi’an 710072; China
 全文: PDF 
摘要： 设$G=(V(G),E(G))$是一个简单连通图, $V(G)$, $E(G)$分别表示图$G$的顶点集和边集. 如果与图$G$同Laplacian谱的图都与$G$同构, 则称图$G$由它的Laplacian谱确定. 该文定义了两类双圈图$Q(n;n_{1},n_2,\cdots ,n_t)$和 $B(n;n_{1},n_{2})$, 证明了双圈图$Q(n;n_{1})$, $Q(n;n_{1},n_{2})$, $Q(n;n_{1},n_{2},n_{3})$和双圈图$B(n;n_{1},n_{2})$分别由它们的Laplacian谱确定.
关键词： Laplacian矩阵;  Laplacian特征多项式;  Laplacian谱    
Abstract: Let $G=(V(G), E(G))$ be a simple connected graph with vertex $V(G)$ and edge set $E(G)$. Two graphs are said to be Laplacian cospectral if they have the same Laplacian spectrum. In this paper, two kinds of bicyclic graphs $Q(n; n_{1}, n_2, \cdots , n_t)$ and $B(n; n_{1}, n_{2})$ are defined. It is proved that graphs $Q(n; n_{1})$, $Q(n; n_{1}, n_{2})$, $Q(n; n_{1}, n_{2}, n_{3})$, and $B(n; n_{1}, n_{2})$ are determined by their Laplacian spectra.
Key words: Laplacian matrix    Laplacian characteristic polynomial    Laplacian spectra
收稿日期: 2015-01-21 出版日期: 2018-05-17
CLC:  O157.5  
基金资助: 国家自然科学基金(11171273); 国家级大学生创新创业训练计划(201410699079)
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王展青
王力工
梅若星
翟若男
董占鹏

引用本文:

王展青, 王力工, 梅若星, 翟若男, 董占鹏. 两类双圈图的Laplacian谱确定问题[J]. 高校应用数学学报, 2016, 31(1): 73-82.

WANG Zhan-qing, WANG Li-gong, MEI Ruo-xing, ZHAI Ruo-nan, DONG Zhan-peng. Two kinds of bicyclic graphs are determined by their Laplacian spectra. Applied Mathematics A Journal of Chinese Universities, 2016, 31(1): 73-82.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2016/V31/I1/73

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