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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (1): 73-82    DOI:
    
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
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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     
Received: 21 January 2015      Published: 17 May 2018
CLC:  O157.5  
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WANG Zhan-qing
WANG Li-gong
MEI Ruo-xing
ZHAI Ruo-nan
DONG Zhan-peng
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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.

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


两类双圈图的Laplacian谱确定问题

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 
[1] WU Bao-feng, PANG Lin-lin, SHEN Fu-qiang. On the least signless Laplacian eigenvalue of graphs[J]. Applied Mathematics A Journal of Chinese Universities, 2016, 31(1): 83-89.