单圈图和双圈图的最大无符号拉普拉斯分离度

doi:10.15960/j.cnki.issn.1007-6093.2015.02.011

Operations Research Transactions ›› 2015, Vol. 19 ›› Issue (2): 99-104.doi: 10.15960/j.cnki.issn.1007-6093.2015.02.011

Previous Articles Next Articles

The maximum signless Laplacian separator of unicyclic and bicyclic graphs

JIAN Xiangguo¹,YUAN Xiying^1,*,ZHANG Man¹

1. Department of Mathematics, College of Sciences,Shanghai University, Shanghai 200444, China

Received:2014-10-02 Online:2015-06-15 Published:2015-06-15

Let G be a graph of order n and q_{1}(G)\geq q_{2}(G)\geq \cdots \geq q_{n}(G) be its Q-eigenvalues. The signless Laplacian separator S_{Q}(G) of G is defined as S_{Q}(G)=q_{1}(G)-q_{2}(G). In this paper, we study the maximum signless Laplacian separator of unicyclic and bicyclic graphs and characterize the extremal graphs, respectively.

Key words: unicyclic graph, bicyclic graph, signless Laplacian separator, signless Laplacian matrix

Cite this article

JIAN Xiangguo,YUAN Xiying,ZHANG Man. The maximum signless Laplacian separator of unicyclic and bicyclic graphs[J]. Operations Research Transactions, 2015, 19(2): 99-104.

share this article

0
/ / Recommend

Add to citation manager EndNote|Reference Manager|ProCite|BibTeX|RefWorks

URL: https://www.ort.shu.edu.cn/EN/10.15960/j.cnki.issn.1007-6093.2015.02.011

https://www.ort.shu.edu.cn/EN/Y2015/V19/I2/99

References

Li J X, Guo J M, Wai C S. On the second largest Laplacian eigenvalues of graphs [J]. Linear Algebra and Its Applications, 2013, 438: 2438-2446.

Kinkar C D. On conjectures involving second largest signless Laplacian eigenvalue of graphs [J]. Linear Algebra and Its Applications, 2010, 432: 3018-3029.

Heuvel J V D. Hamilton cycles and eigenvalues of graphs [J]. Linear Algebra and Its Applications, 1995, 226-228: 723-730.

Oliverira C, Lina L, Abreu N, et al. Bounds on the index of the signless Laplacian of a graph [J]. Discrete Applied Mathematics, 2010, 158(2): 355-360.

Cvetkovi \acute{c} D, Doob D, Sachs M H. Spectra of Graphs-Theory and Application [M]. Heidelberg-Leipzig: Johann Ambrosius Barth Verlag, 1995.

Yuan X Y. A note on the Laplacian spectral radii of bicyclic graphs [J]. Advances in Mathematics, 2010, 39(6): 703-708.

Related Articles 7

[1]	TAO Yanliang, HUANG Qiongxiang, CHEN Lin. Contraction graph method for the interval edge-colorings of graphs [J]. Operations Research Transactions, 2019, 23(2): 31-43.
[2]	SUN Qiushi, YANG Xiaoyun, WANG Ligong, LI Xihe, WANG Pengchao. Laplacian spectral characterizations of new unicyclic graphs H(p,tK_1,m) [J]. Operations Research Transactions, 2019, 23(1): 72-80.
[3]	ZHAI Ruonan, WANG Ligong, DONG Zhanpeng, WANG Zhanqing, MEI Ruoxing. Laplacian spectral characterizations of some classes of multi-cyclic graphs [J]. Operations Research Transactions, 2016, 20(2): 59-68.
[4]	MEI Ruoxing, WANG Ligong, WANG Luhua, WANG Zhanqing. Laplacian spectral characterizations of unicyclic graphs H( p, t K_{ 1, m}) [J]. Operations Research Transactions, 2015, 19(1): 57-64.
[5]	XIAO Mao, WANG Wenhuan. Minimal skew energies of oriented bicyclic graphs without even cycles [J]. Operations Research Transactions, 2014, 18(4): 85-95.
[6]	CHEN Lin, HUANG Qiongxiang. Tricyclic graphs with exactly two Q-main eigenvalues [J]. Operations Research Transactions, 2014, 18(3): 13-32.
[7]	XU Weiwei, WANG Wenhuan. Bicyclic graph with the maximal Estrada indices [J]. Operations Research Transactions, 2014, 18(2): 111-118.

Metrics

Viewed

Full text

Abstract

Comments

Abstract
References
Related Articles
Recommended Articles
Metrics
Comments

TOP

The maximum signless Laplacian separator of unicyclic and bicyclic graphs

PDF

Knowledge

Abstract