图的广义距离谱

doi:10.6040/j.issn.1671-9352.0.2019.766

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (9): 19-28.doi: 10.6040/j.issn.1671-9352.0.2019.766

• • 上一篇

图的广义距离谱

卢鹏丽^*,刘文智

兰州理工大学计算机与通信学院, 甘肃兰州 730050

发布日期:2020-09-17
作者简介:卢鹏丽(1973— ),女,博士,教授,博士生导师,研究方向为图论与复杂网络. E-mail:lupengli88@163.com*通信作者

On the generalized distance spectrum of graphs

LU Peng-li^*, LIU Wen-zhi

School of Computer and Communication, Lanzhou University of Technology, Lanzhou 730050, Gansu, China

Published:2020-09-17

摘要/Abstract

摘要： 基于一些图参数得到了图G及其线图L(G)广义距离谱半径的上下界,并确定了极值图;然后计算了一些合成图的广义距离谱。

关键词: 广义距离矩阵, 谱半径, 传递度, 图操作, 线图

Abstract: The upper and lower bounds of the generalized distance spectral radius of G and of its line graph L(G)are obtained, based on some graph parameters, and the extremal graphs are determined. Then, the generalized distance spectrum of some composite graphs is calculated.

Key words: generalized distance matrix, spectral radius, transmission degree, graph operations, line graph

中图分类号:

O157.5

卢鹏丽,刘文智. 图的广义距离谱[J]. 《山东大学学报(理学版)》, 2020, 55(9): 19-28.

LU Peng-li, LIU Wen-zhi. On the generalized distance spectrum of graphs[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(9): 19-28.

参考文献

[1] AOUCHICHE M, HANSEN P. Two Laplacians for the distance matrix of a graph[J]. Linear Algebra and Its Applications, 2013, 430:21-33.
[2] TIAN Guixian, CUI Shuyu, HE Jingxiang. The generalized distance matrix[J]. Linear Algebra and Its Applications, 2019, 563:1-23.
[3] CVETKOVIC D M, DOOB M, SACHS H. Spectra of graphs-theory and application[M]. New York: Academic Press, 1980.
[4] WOODHOUSE J H. On Rayleighs principle[J]. Geophysical Journal International, 2007, 46(1):11-22.
[5] AOUCHICHE M, HANSEN P. Distance spectra of graphs: a survey[J]. Linear Algebra and Its Applications, 2014, 458:301-386.
[6] AOUCHICHE M, HANSEN P. Some properties of the distance Laplacian eigenvalues of a graph[J]. Czechoslovak Math, 2014, 64:751-761.
[7] ALHEVAZ A, BAGHIPUR M, HASHEMI E, On the distance signless Laplacian spectrum of graphs[J]. Bulletin of the Malaysian Mathematical Sciences Society, 2018. https://doi.org/10.1007/s40840-018-0619-8.
[8] ROBERTO C D, GERMAIN P, OSCAR R. New results on the Dα-matrix of connected graphs[J]. Linear Algebra and Its Applications, 2019, 577:168-185.
[9] LIN Huiqiu, LU Xiwen. Bounds on the distance signless Laplacian spectral radius in terms of clique number[J]. Linear Multilinear Algebra, 2015, 63:1750-1759.
[10] NIU Aihong,FAN Dandan,WANG Guoping. On the distance Laplacian spectral radius of bipartite graphs[J]. Discrete Appl Math, 2015, 186:207-213.
[11] TIAN Fenglei, WONG Dein, ROU Jianling. Proof for four conjectures about the distance Laplacian and distance signless Laplacian eigenvalues of a graph[J]. Linear Algebra Appl, 2015, 471:10-20.
[12] XING Rundan, ZHOU Bo, LI Jianping. On the distance signless Laplacian spectral radius of graphs[J]. Linear Multilinear Algebra, 2014, 62:1377-1387.
[13] MADEN A D, DAS K C, CEVIK A S. Sharp upper bounds on the spectral radius of the signless Laplacian matrix of a graph[J]. Appl Math Comput, 2013, 219:5025-5032.
[14] LASKAR R. Eigenvalues of the adjacency matrix of cubic lattice graphs[J]. Pacific Journal of Mathematics, 1969, 29:623-629.
[15] HARARY F. Graph theory[M]. New Delhi: Narosa Publishing House, 1999.
[16] MINC H. Nonnegative matrices[M]. New York: Wiley, 1988.
[17] RAMANE H S, GUTMAN I, GANAGI A B. On diameter of line graphs[J]. Iranian Journal of Mathematical Sciences and Informatics, 2013, 8:105-109.
[18] RAMANE H S, GUTMAN I, REVANKAR D S, et al. Distance spectra and distance energies of iterated line graphs of regular graphs[J]. Publ Inst Math, 2009, 85:39-46.
[19] FOWLER P W, CAPOROSSI G, HANSEN P. Distance matrices, Wiener indices, and related invariants of fullerenes[J]. J Phys Chem A, 2001, 105:6232-6242.
[20] INDULAL G. Distance spectrum of graph compositions[J]. ARS Mathematica Contemporanea, 2009, 2:93-100.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

图的广义距离谱

On the generalized distance spectrum of graphs

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 5

多维度评价

本文评价

推荐阅读 0

[1]	薛秋芳1,2,高兴宝1*,刘晓光1. H-矩阵基于外推GaussSeidel迭代法的几个等价条件[J]. J4, 2013, 48(4): 65-71.
[2]	王万禹,孟吉翔*,赵雪冰. 线图的限制性邻域连通度[J]. J4, 2012, 47(2): 56-59.
[3]	刘晓光,畅大为*. 亏秩线性方程组PSD迭代法的最优参数[J]. J4, 2011, 46(12): 13-18.
[4]	邹黎敏1, 姜友谊1，胡兴凯2. 关于矩阵Frobenius范数的一个猜想[J]. J4, 2010, 45(4): 48-50.
[5]	冯立华,于桂海 . 与图谱有关的一个图兰定理[J]. J4, 2008, 43(6): 31-33 .