References

  1. Anderson D.F., Livingston P.S. The zero divisor graph of a commutative ring. J. Algebra 1999, 217 (2), 434–447. doi:10.1006/jabr.1998.7840
  2. Aouchiche M., Hansen P. Two Laplacians for the distance matrix of a graph. Linear Algebra Appl. 2013, 439 (1), 21–33. doi:10.1016/j.laa.2013.02.030
  3. Aouchiche M., Hansen P. Some properties of the distance Laplacian eigenvalues a graph. Czechoslovak Math. J. 2014, 64 (3), 751–761. doi:10.1007/s10587-014-0129-2
  4. Atiyah M.F., MacDonald I.G. Introduction to Commutative Algebra. Addison Wesley Publ., Boston, 1994.
  5. Chattopadhyay S., Patra K.L., Sahoo B.K. Laplacian eigenvalues of the zero divisor graph of the ring \(\mathbb{Z}_{n}\). Linear Algebra Appl. 2020, 584, 267–286. doi:10.1016/j.laa.2019.08.015
  6. Cvetković D.M., Rowlinson P., Simić S. An Introduction to Theory of Graph spectra. Cambridge University Press, Cambridge, 2010. doi:10.1017/CBO9780511801518
  7. Ganie H.A. On distance Laplacian spectrum (energy) of graphs. Discrete Math. Algorithms Appl. 2020, 12 (5), 2050061. doi:10.1142/S1793830920500615
  8. Horn R., Johnson C. Matrix Analysis. Cambridge University Press, Cambridge, 2013.
  9. Young M. Adjacency matrices of zero divisor graphs of integer modulo \(n\). 2015, Involve 8 (5), 753–761. doi:10.2140/involve.2015.8.753
  10. Pirzada S. An Introduction to Graph Theory. Universities Press, Orient BlackSwan, Hyderabad, 2012.
  11. Pirzada S., Rather B.A., Aijaz M., Chishti T.A. On distance signless Laplacian spectrum of graphs and spectrum of zero divisor graphs of \(\mathbb{Z}_n\). Linear Multilinear Algebra 2020. doi:10.1080/03081087.2020.1838425
  12. Pirzada S., Rather B.A., Shaban R.U., Merajuddin. On signless Laplacian spectrum of the zero divisor graphs of the ring \(\mathbb{Z}_{n}\). Korean J. Math. 2021, 29 (1), 13–24.
  13. Rather B.A., Pirzada S., Naikoo T.A., Shang Y. On Laplacian eigenvalues of the zero-divisor graph associated to the ring of integers modulo \(n\). Mathematics 2021, 9 (5), 482. doi:10.3390/math9050482
  14. Stevanović D. Large sets of long distance equienergetic graphs. Ars Math. Contemp. 2009, 2 (1), 35–40. doi:10.26493/1855-3974.93.e75