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[1]石 超,王秀雯,郑艺容*.一致超树的邻接张量的Z-谱半径[J].厦门大学学报(自然科学版),2019,58(04):547-549.[doi:10.6043/j.issn.0438-0479.201806020]
 SHI Chao,WANG Xiuwen,ZHENG Yirong*.Z-spectral radius of the adjacency tensor of uniform supertrees[J].Journal of Xiamen University(Natural Science),2019,58(04):547-549.[doi:10.6043/j.issn.0438-0479.201806020]
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《厦门大学学报(自然科学版)》[ISSN:0438-0479/CN:35-1070/N]

卷:
58卷
期数:
2019年04期
页码:
547-549
栏目:
研究论文
出版日期:
2019-07-28

文章信息/Info

Title:
Z-spectral radius of the adjacency tensor of uniform supertrees
文章编号:
0438-0479(2019)04-0547-03
作者:
石 超1王秀雯1郑艺容2*
1.厦门大学嘉庚学院信息科学与技术学院,福建 漳州 363105; 2.厦门理工学院应用数学学院,福建 厦门 361024
Author(s):
SHI Chao1WANG Xiuwen1ZHENG Yirong2*
1.School of Information Science and Technology,Xiamen University Tan Kah Kee College,Zhangzhou 363105,China; 2.College of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,China
关键词:
一致超树 邻接张量 Z-特征值 Z-谱半径
Keywords:
uniform supertrees adjacency tensor Z-eigenvalues Z-spectral radius
分类号:
O 157.6
DOI:
10.6043/j.issn.0438-0479.201806020
文献标志码:
A
摘要:
T是任意给定的r一致超树,ρ<sub>Z(T)是T的邻接张量的Z-谱半径.证明了当r≥3时,ρ</sub>Z(T)=r1-r/2.
Abstract:
Let T be an r-uniform supertree,and ρ</sub>Z(T)be the Z-spectral radius of the adjacency tensor of T. We show that ρ</sub>Z(T)=r1-r/2 with r≥3.

参考文献/References:

[1] BROUWER A E,HAEMERS W H.Spectra of graphs[M].Berlin:Springer Science and Business Media,2011:3-9.
[2] QI L.Eigenvalues of a real supersymmetric tensor[J].J Symb Compute,2005,40:1302-1324.
[3] LIM L H.Singular values and eigenvalues of tensors:a variational approach[C]∥Proc IEEE International Workshop on Computational Advances in Muli-tensor Adaptive Prcocessing(CAMSAP’05).Puerto Vallarta:IEEE,2005:129-132.
[4] QI L,YW G,WU E.Higher oder positive semi-definite diffusion tensor imaging[J].SIAM J Imaging Sci,2010,3(3):416-433.
[5] COOPER J,DUTLE A.Spectra of uniform hypergraphs[J].Linear Algebra Appl,2012,436:3268-3292.
[6] BERGE C.Hypergraphs,combinatorics of finite sets[M].Amsterdam:Elsevier,1984:1-30.
[7] LI H,SHAO J,QI L.The extremal spectral radii of k-uniform supertrees[J].J Comb Optim,2016,32:741-764.
[8] CHANG K C,QI L,ZHANG T.A survey on the spectral theory of nonnegative tensors[J].Numer Linear Algebra Appl,2013,20:891-912.
[9] CHANG K C,PEARSON K,ZHANG T.Some variational principles of the Z-eigenvalues for nonnegative tensors[J].Linear Algebra Appl,2013,438:416-4182.
[10] NIKIFOROV V.Analytic methods for uniform hypergraphs[J].Linear Algebra Appl,2014,457:455-535.
[11] XIE J,CHANG A.On the Z-eigenvalues of the adjacency tensors for uniform hypergraphs[J].Linear Algebra Appl,2013,439:2195-2204.[1] BROUWER A E,HAEMERS W H.Spectra of graphs[M].Berlin:Springer Science and Business Media,2011:3-9.
[2] QI L.Eigenvalues of a real supersymmetric tensor[J].J Symb Compute,2005,40:1302-1324.
[3] LIM L H.Singular values and eigenvalues of tensors:a variational approach[C]∥Proc IEEE International Workshop on Computational Advances in Muli-tensor Adaptive Prcocessing(CAMSAP’05).Puerto Vallarta:IEEE,2005:129-132.
[4] QI L,YW G,WU E.Higher oder positive semi-definite diffusion tensor imaging[J].SIAM J Imaging Sci,2010,3(3):416-433.
[5] COOPER J,DUTLE A.Spectra of uniform hypergraphs[J].Linear Algebra Appl,2012,436:3268-3292.
[6] BERGE C.Hypergraphs,combinatorics of finite sets[M].Amsterdam:Elsevier,1984:1-30.
[7] LI H,SHAO J,QI L.The extremal spectral radii of k-uniform supertrees[J].J Comb Optim,2016,32:741-764.
[8] CHANG K C,QI L,ZHANG T.A survey on the spectral theory of nonnegative tensors[J].Numer Linear Algebra Appl,2013,20:891-912.
[9] CHANG K C,PEARSON K,ZHANG T.Some variational principles of the Z-eigenvalues for nonnegative tensors[J].Linear Algebra Appl,2013,438:416-4182.
[10] NIKIFOROV V.Analytic methods for uniform hypergraphs[J].Linear Algebra Appl,2014,457:455-535.
[11] XIE J,CHANG A.On the Z-eigenvalues of the adjacency tensors for uniform hypergraphs[J].Linear Algebra Appl,2013,439:2195-2204.

备注/Memo

备注/Memo:
收稿日期:2018-06-19 录用日期:2019-03-18
基金项目:国家自然科学基金(11471077)
*通信作者:yrzheng@xmut.edu.cn
更新日期/Last Update: 1900-01-01