Remark on bounds for the Laplacian spread of a graph

[1] B. Afshari and S. Akbari, Some results on the Laplacian spread conjecture, Linear Algebra Appl. 574 (2019), 22–29. https://doi.org/10.1016/j.laa.2019.03.003

[2] E. Andrade, D.M. Cardoso, M. Robbiano, and J. Rodríguez, Laplacian spread of graphs: Lower bounds and relations with invariant parameters, Linear Algebra Appl. 486 (2015), 494–503. https://doi.org/10.1016/j.laa.2015.08.027

[3] E. Andrade, H. Gomes, M. Robbiano, and J. Rodr´ıguez, Upper bounds on the
Laplacian spread of graphs, Linear Algebra Appl. 492 (2016), 26–37.
https://doi.org/10.1016/j.laa.2015.11.010.
[4] Y.H. Bao, Y.Y. Tan, and Y.Z. Fan, The Laplacian spread of unicyclic graphs,
Appl. Math. Lett. 22 (2009), no. 7, 1011–1015.
https://doi.org/10.1016/j.aml.2009.01.023.
[5] W. Barrett, E. Evans, H.T. Hall, and M. Kempton, New conjectures on algebraic
connectivity and the Laplacian spread of graphs, Linear Algebra Appl. 648 (2022),
104–132.
https://doi.org/10.1016/j.laa.2022.04.021.
[6] M.A. Bhat and P.A. Manan, Bounds for the trace norm of Aα matrix of digraphs,
Discrete Math. 348 (2025), no. 8, 114491.
https://doi.org/10.1016/j.disc.2025.114491.
[7] X. Chen and K.C. Das, Some results on the Laplacian spread of a graph, Linear
Algebra Appl. 505 (2016), 245–260.
https://doi.org/10.1016/j.laa.2016.05.002.
[8] D. Cvetkovi´c, P. Rowlinson, and S. Simi´c, An introduction to the theory of graph
spectra, Cambridge Univ. Press, Cambridge, 2009.
[9] K.C. Das, A sharp upper bound for the number of spanning trees of a graph,
Graphs Combin. 23 (2007), no. 6, 625–632.
https://doi.org/10.1007/s00373-007-0758-4.
[10] Y.Z. Fan, J. Xu, Y. Wang, and D. Liang, The Laplacian spread of a tree, Discrete
Math. Theor. Comput. Sci. 10 (2008), 79–86.
https://doi.org/10.46298/dmtcs.439.
[11] M. Fiedler, Algebraic connectivity of graphs, Czechoslovak Math. J. 23 (1973),
no. 2, 298–305.
https://doi.org/10.21136/CMJ.1973.101168.
[12] R. Grone and R. Merris, The Laplacian spectrum of a graph II, SIAM J. Discrete
Math. 7 (1994), no. 2, 221–229.
https://doi.org/10.1137/S0895480191222653.
[13] I. Gutman and K.C. Das, The first Zagreb index 30 years after, MATCH Com-
mun. Math. Comput. Chem. 50 (2004), no. 1, 83–92.
[14] R. Merris, Laplacian matrices of graphs: A survey, Linear Algebra Appl. 197
(1994), 143–176.
https://doi.org/10.1016/0024-3795(94)90486-3.
[15] S. Pirzada, R. Ul Shaban, H. A. Ganie, and L. de Lima, On the Ky Fan norm of
the signless Laplacian matrix of a graph, Comput. Appl. Math. 43 (2024), no. 1,
Paper No. 26.
[16] V. M. Preciado, A. Jadbabaie, and G.C. Verghese, Structural analysis of Lapla-
cian spectral properties of large-scale networks, IEEE Trans. Automat. Control
58 (2013), no. 9, 2338–2343.
[17] Z. Stanić, Inequalities for graph eigenvalues, Cambridge Univ. Press, Cambridge,
2015.
[18] Z. You and B. Liu, The Laplacian spread of graphs, Czechoslovak Math. J. 62 (2012), no. 1, 155–168. https://doi.org/10.1007/s10587-012-0003-z