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高校应用数学学报
高校应用数学学报  2014, Vol. 29 Issue (3): 295-302    
    
不含三圈的$k$圈图的拟拉普拉斯和拉普拉斯谱半径
何春阳1,2, 郭曙光2
1. 青海师范大学 数学系, 青海西宁 810008
2. 盐城师范学院 数学科学学院, 江苏盐城 224002
On the signless Laplacian and Laplacian spectral radius of triangle-free $k$-cyclic graphs
HE Chun-yang1,2, GUO Shu-guang2
1. Department of Mathematics, Qinghai Normal University, Xining 810008, China
2. School of Mathematical Sciences, Yancheng Teachers University, Yancheng 224002, China
 全文: PDF 
摘要： $k$圈图是边数等于顶点数加$k-1$的简单连通图. 文中确定了不含三圈的$k$圈图的拟拉普拉斯谱半径的上界，并刻画了达到该上界的极图. 此外, 文中确定了拟拉普拉斯谱半径排在前五位的不含三圈的单圈图, 排在前八位的不含三圈的双圈图. 最后说明文中所得结论对不含三圈的$k$圈图的拉普拉斯谱半径也成立.
关键词： $k$圈图;  不含三圈;  拟拉普拉斯谱半径;  拉普拉斯谱半径;  单圈图;  双圈图    
Abstract: A $k$-cyclic graph is a connected graph in which the number of edges equals the number of vertices plus $k+1$. This paper determines the maximal signless Laplacian spectral radius together with the corresponding extremal graph among all triangle-free $k$-cyclic graphs of order $n$. Moreover, this paper gives the first five triangle-free unicyclic graphs on $n \,(n\geq 8)$ vertices, and the first eight triangle-free bicyclic graphs on $n \,(n\geq 12)$ vertices according to the signless Laplacian spectral radius. Finally, the authors of this paper show that the results obtained in this paper also hold for Laplacian spectral radius of triangle-free $k$-cyclic graphs of order $n$.
Key words: $k$-cyclic graph    triangle-free    signless Laplacian spectral radius    Laplacian spectral radius    unicyclic graph    bicyclic graph
收稿日期: 2014-04-08 出版日期: 2018-06-10
CLC:  O157  
基金资助: 国家自然科学基金(11171290)
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引用本文:

何春阳, 郭曙光. 不含三圈的$k$圈图的拟拉普拉斯和拉普拉斯谱半径[J]. 高校应用数学学报, 2014, 29(3): 295-302.

HE Chun-yang, GUO Shu-guang. On the signless Laplacian and Laplacian spectral radius of triangle-free $k$-cyclic graphs. Applied Mathematics A Journal of Chinese Universities, 2014, 29(3): 295-302.

链接本文:

http://www.zjujournals.com/amjcua/CN/    或    http://www.zjujournals.com/amjcua/CN/Y2014/V29/I3/295

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