《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
卢鹏丽*,刘文智
LU Peng-li*, LIU Wen-zhi
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。
中图分类号:
| [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 Rayleighs 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. |
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