312
Views
6
CrossRef citations to date
0
Altmetric
Articles

On spectral spread of generalized distance matrix of a graph

ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 2819-2835 | Received 12 Oct 2019, Accepted 19 Aug 2020, Published online: 06 Sep 2020

References

  • Brouwer A, Haemers W. Spectra of GraphsSpringer; 2012.
  • Pirzada S. An introduction to graph theory. Hyderabad: Universities Press, Orient Black Swan; 2012.
  • Aouchiche M, Hansen P. Distance spectra of graphs: a survey. Linear Algebra Appl. 2014;458:301–386. doi: 10.1016/j.laa.2014.06.010
  • Aouchiche M, Hansen P. Two Laplacians for the distance matrix of a graph. Linear Algebra Appl. 2013;439:21–33. doi: 10.1016/j.laa.2013.02.030
  • Aouchiche M, Hansen P. On the distance signless Laplacian of a graph. Linear Multilinear Algebra. 2016;64:1113–1123. doi: 10.1080/03081087.2015.1073215
  • Aouchiche M, Hansen P. Some properties of distance Laplacian spectra of a graph. Czechoslovak Math J. 2014;64:751–761. doi: 10.1007/s10587-014-0129-2
  • Alhevaz A, Baghipur M, Ganie HA, et al. Brouwer type conjecture for the eigenvalues of distance signless Laplacian matrix of a graph. Linear Multilinear Algebra. 2019. [cited 2019 Nov 12]. Available from: https://doi.org/10.1080/03081087.2019.1679074
  • Alhevaz A, Baghipur M, Hashemi E. Further results on the distance signless Laplacian spectrum of graphs. Asian-Euro J Math. 2018;11:1850067. doi: 10.1142/S1793557118500663
  • Aouchiche M, Hansen P. Distance Laplacian eigenvalues and chromatic number in graphs. Filomat. 2017;31:2545–2555. doi: 10.2298/FIL1709545A
  • Aouchiche M, Hansen P. Cospectrality of graphs with respect to distance matrices. Appl Math Comput. 2018;325:309–321.
  • Atik F, Panigrahi P. On the distance and distance signless Laplacian eigenvalues of graphs and the smallest Gerŝgorin disc. Elect J Linear Algebra. 2018;34:191–204. doi: 10.13001/1081-3810.3510
  • Lin H, Zhou B. On the distance Laplacian spectral radius of graphs. Linear Algebra Appl. 2015;475:265–275. doi: 10.1016/j.laa.2015.02.033
  • Ma X, Qi L, Tian F, et al. Graphs with some distance Laplacian eigenvalue of multiplicity n−3. Linear Algebra Appl. 2018;557:307–326. doi: 10.1016/j.laa.2018.07.033
  • Stevanović D, Ilić A. Spectral properties of distance matrix of graphs, Mathematical Chemistry Monographs. In: Gutman I, Furtula B, editors. Distance in molecular graphs-theory. Kragujevac: Univ. Kragujevac; 2012. p. 139–176.
  • You L, Ren L, Yu G. Distance and distance signless Laplacian spread of connected graphs. Discrete Appl Math. 2017;223:140–147. doi: 10.1016/j.dam.2016.12.030
  • Cui SY, He JX, Tian GX. The generalized distance matrix. Linear Algebra Appl. 2019;563:1–23. doi: 10.1016/j.laa.2018.10.014
  • Lin H, Xue J, Shu J. On the Dα-spectra of graphs. Linear Multilinear Algebra. 2019. [cited 2019 may 22]. Available from: https://doi.org/10.1080/03081087.2019.1618236
  • Alhevaz A, Baghipur M, Ganie HA, et al. On the generalized distance energy of graphs. Mathematics. 2020;8. Article 17. doi: 10.3390/math8030426
  • Alhevaz A, Baghipur M, Ganie HA, et al. Bounds for the generalized distance eigenvalues of a graph. Symmetry. 2019;11: Article 1529.
  • Yu G, Zhang H, Lin H, et al. Distance spectral spread of a graph. Discr Appl Math. 2012;160:2474–2478. doi: 10.1016/j.dam.2012.05.015
  • Horn R, Johnson C. Matrix analysis. Cambridge: Cambridge University Press; 1985.
  • So W. Commutativity and spectra of Hermitian matrices. Linear Algebra Appl. 1994;212/213:121–129. doi: 10.1016/0024-3795(94)90399-9
  • Indulal G. Sharp bounds on the distance spectral radius and the distance energy of graphs. Linear Algebra Appl. 2009;430:1061–113. doi: 10.1016/j.laa.2008.07.005
  • Mirsky L. The spread of a matrix. Mathematika. 1956;3:127–130. doi: 10.1112/S0025579300001790
  • Cvetković D, Doob M, Sachs H. Spectra of graphs-theory and applications. New York: Academic Press, Inc.; 1980. (Pure and Applied Mathematics, 87).

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.