[1]何 军,刘衍民,冉 杰.有向图的无符号拉普拉斯谱半径的新上下界[J].四川师范大学学报(自然科学版),2018,(03):348-350.[doi:10.3969/j.issn.1001-8395.2018.03.012]
 HE Jun,LIU Yanmin,RAN Jie.Some New Upper and Lower Boundon the Spectral Radius of the Signless Laplacian Matrix of a Digraph[J].Journal of SichuanNormal University,2018,(03):348-350.[doi:10.3969/j.issn.1001-8395.2018.03.012]
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有向图的无符号拉普拉斯谱半径的新上下界()
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年03期
页码:
348-350
栏目:
基础理论
出版日期:
2018-03-15

文章信息/Info

Title:
Some New Upper and Lower Boundon the Spectral Radius of the Signless Laplacian Matrix of a Digraph
文章编号:
1001-8395(2018)03-0348-03
作者:
何 军1 刘衍民2 冉 杰3
遵义师范学院 数学学院, 贵州 遵义 563006
Author(s):
HE Jun LIU Yanmin RAN Jie
School of Mathematics, Zunyi Normal College, Zunyi 563006, Guizhou
关键词:
有向图 无符号拉普拉斯矩阵 谱半径
Keywords:
digraph signless Laplacian matrix spectral radius
分类号:
O157.5
DOI:
10.3969/j.issn.1001-8395.2018.03.012
文献标志码:
A
摘要:
设G是一个n 阶的简单有向连通图,令A(G)为有向图G的邻接矩阵,D(G)为有向图G的出度对角矩阵,则有向图G的无符号拉普拉斯矩阵可以表示为Q(G)=A(G)+D(G).利用图中顶点vi的出度d+i和平均二次出度m+i,给出一些有向图G的无符号拉普拉斯矩阵谱半径q1(G)更精细化的上下界,并通过数值例子证实新上下界的有效性.
Abstract:
Let G be a simple connected digraph, A(G) denote its adjacency matrix, and D(G) denote the diagonal matrix of its vertex out degrees, then the signless Laplacian matrix of G is Q(G)=A(G)+D(G). In this paper, we obtain some new upper and lower bound on the spectral radius q1(G) of the signless Laplacian matrix of a digraph G. A numerical example is given to show the efficiency of our new results.

参考文献/References:

[1] CVETKOVIC D, DOOB M, SACHS H. Spectra of Graphs[M]. New York:Academic Press,1980.
[2] SHU J L, HONG Y, WEN R K. A sharp upper bound on the largest eigenvalue of the Laplacian matrix of a graph[J]. Linear Algebra Appl,2002,347(1/2/3):123-129.
[3] YAN C. Properties of spectra of graphs and line graphs[J]. Appl Math J Chin Uni,2002,17(3):371-376.
[4] XI W G, WANG L G. Sharp upper bounds on the signless Laplacian spectral radius of strongly connected digraphs[J]. Discussiones Mathematicae Graph Theory,2016,36(4):977-988.
[5] HORN A, JOHNSON C R. Matrix Analysis[M]. New York:Cambridge University Press,2013.
[6] BOZKURT S B, BOZKURT D. On the signless Laplacian spectral radius of digraphs[J]. Ars Combinatoria,2013,108(108):193-200.

备注/Memo

备注/Memo:
收稿日期:2017-04-24 接受日期:2017-06-20
基金项目:国家自然科学基金(71461027)、贵州省科技厅基础研究项目基金(黔科合基础[2016]1161)、贵州省教育厅自然科学基金(黔教合KY KY [2016]255)和贵州省科技厅联合基金(黔科合LH字[2016]7032号)
第一作者简介:何 军(1981—),男,副教授,主要从事数值代数的研究,E-mail:hejunfan1@163.com
更新日期/Last Update: 2018-03-15