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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2016, Vol. 31 Issue (1): 83-89    DOI:
    
On the least signless Laplacian eigenvalue of graphs
WU Bao-feng, PANG Lin-lin, SHEN Fu-qiang
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
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Abstract  A class of graphs constructed by $H$ and $K_s$ was studied, where $H$ is a bipartite graph of order $n$ and $K_s$ is the complete graph of order $s$. It was shown that a sharp upper bound of the least signless Laplacian eigenvalue (the least $Q$-eigenvalue) is $s$. Based on this, for any given positive integer $s$ and positive even number $n$, a class of graphs of order $n+s$ was constructed which have eigenvalue $s$ as their least $Q$-eigenvalue. Also, for any given smallest degree $\delta$ and order $n$ such that $2\leq\delta\leq\frac{n-1}{2}$, a class of graphs of order $n$ was constructed which have eigenvalue $\delta-1$ as their least $Q$-eigenvalue.

Key words： signless Laplacian matrix      least $Q$-eigenvalue      bound      smallest degree     
Received: 24 May 2015      Published: 17 May 2018
CLC:  O157.5  
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WU Bao-feng
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SHEN Fu-qiang
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WU Bao-feng, PANG Lin-lin, SHEN Fu-qiang. On the least signless Laplacian eigenvalue of graphs. Applied Mathematics A Journal of Chinese Universities, 2016, 31(1): 83-89.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2016/V31/I1/83


关于图的最小$Q$-特征值

研究了基于$n$阶二部图和$s$阶完全图构造的一个图类, 得到了该图类的无符号拉普拉斯最小特征值(即最小$Q$-特征值)的一个可达上界为$s$. 基于此, 对于任意给定的正整数$s$和正偶数$n$, 构造了最小$Q$-特征值为$s$的一类$n+s$阶图. 另外, 对于任意给定的最小度$\delta$和阶数$n$, 在满足$2\leq\delta\leq\frac{n-1}{2}$条件下, 构造了最小$Q$-特征值为$\delta-1$的一类$n$阶图.

关键词： 无符号拉普拉斯矩阵,  最小$Q$-特征值,  界,  最小度 
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