References
- Cvetković D, Rowlinson P, Simić S. An introduction to the theory of graph spectra. Cambridge: Cambridge University Press; 2010.
- Doob M. Graphs with a small number of distinct eigenvalues. Ann New York Acad Sci. 1970;175:104–110. doi: https://doi.org/10.1111/j.1749-6632.1970.tb56460.x
- Cheng XM, Gavrilyuk AL, Greaves GRW, et al. Biregular graphs with three eigenvalues. Eur J Comb. 2016;56:57–80. doi: https://doi.org/10.1016/j.ejc.2016.03.004
- Cheng XM, Greaves GRW, Koolen JH. Graphs with three eigenvalues and second largest eigenvalue at most 1. J Comb Theor Ser B. 2018;129:55–78. doi: https://doi.org/10.1016/j.jctb.2017.09.004
- Cioabă SM, Haemers WH, Vermette JR, et al. The graphs with all but two eigenvalues equal to ±1. J. Algebraic Comb. 2015;41(3):887–897. doi: https://doi.org/10.1007/s10801-014-0557-y
- Cioabă SM, Haemers WH, Vermette JR. The graphs with all but two eigenvalues equal to −2 or 0. Des Codes Cryptogr. 2017;84(1–2):153–163. doi: https://doi.org/10.1007/s10623-016-0241-4
- de Caen D, van Dam ER, Spence E. A nonregular analogue of conference graphs. J Comb Theor Ser A. 1999;88:194–204. doi: https://doi.org/10.1006/jcta.1999.2983
- Ghorbani E. Bipartite graphs with five eigenvalues and pseudo designs. J Algebraic Comb. 2012;36:209–221. doi: https://doi.org/10.1007/s10801-011-0331-3
- Hayat S, Javaid M, Koolen JH. Graphs with two main and two plain eigenvalues. Appl Anal Discrete Math. 2017;11:244–257. doi: https://doi.org/10.2298/AADM1702244H
- Huang X, Huang Q. On regular graphs with four distinct eigenvalues. Linear Algebra Appl. 2017;512:219–233. doi: https://doi.org/10.1016/j.laa.2016.09.043
- Rowlinson P. On graphs with just three distinct eigenvalues. Linear Algebra Appl. 2016;507:462–473. doi: https://doi.org/10.1016/j.laa.2016.06.031
- van Dam ER. Regular graphs with four eigenvalues. Linear Algebra Appl. 1995;226–228:139–163. doi: https://doi.org/10.1016/0024-3795(94)00346-F
- van Dam ER. Nonregular graphs with three eigenvalues. J Comb Theor Ser B. 1998;73:101–118. doi: https://doi.org/10.1006/jctb.1998.1815
- van Dam ER, Spence E. Combinatorial designs with two singular values I: uniform multiplicative designs. J Combi Theor Ser A. 2004;107:127–142. doi: https://doi.org/10.1016/j.jcta.2004.04.004
- Mohammadian A, Tayfeh-Rezaie B. Graphs with four distinct Laplacian eigenvalues. J Algebraic Comb. 2011;34(4):671–682. doi: https://doi.org/10.1007/s10801-011-0287-3
- van Dam ER, Haemers WH. Graphs with constant μ and μ¯. Discrete Math. 1998;182:293–307. doi: https://doi.org/10.1016/S0012-365X(97)00150-7
- Wang Y, Fan Y, Tan Y. On graphs with three distinct Laplacian eigenvalues. Appl Math J Chin Univ Ser B. 2007;22:478–484. doi: https://doi.org/10.1007/s11766-007-0414-z
- Ayoobi F, Omidi GR, Tayfeh-Rezaie B. A note on graphs whose signless Laplacian has three distinct eigenvalues. Linear Multilinear Algebra. 2011;59(6):701–706. doi: https://doi.org/10.1080/03081087.2010.489900
- Cavers M. The normalized Laplacian matrix and general Randić Index of Graphs [thesis]. University of Regina; Regina; 2010.
- Huang X, Huang Q. On graphs with three or four distinct normalized Laplacian eigenvalues. Algebra Colloq. 2019;26(1):65–82. doi: https://doi.org/10.1142/S1005386719000075
- van Dam ER, Omidi GR. Graphs whose normalized Laplacian has three eigenvalues. Linear Algebra Appl. 2011;435:2560–2569. doi: https://doi.org/10.1016/j.laa.2011.02.005
- Huang X, Huang Q, Lu L. Graphs with at most three distance eigenvalues different from −1 and −2. Graphs Comb. 2018;34(3):395–414. doi: https://doi.org/10.1007/s00373-018-1880-1
- Koolen JH, Hayat S, Iqbal Q. Hypercubes are determined by their distance spectra. Linear Algebra Appl. 2015;505:97–108. doi: https://doi.org/10.1016/j.laa.2016.04.036
- Lu L, Huang Q, Huang X. The graphs with exactly two distance eigenvalues different from −1 and −3. J Algebra Comb. 2017;45:629–647. doi: https://doi.org/10.1007/s10801-016-0718-2
- Lu L, Huang Q, Huang X. On graphs whose smallest distance (signless Laplacian) eigenvalue has large multiplicity. Linear Multilinear Algebra. 2018;66(11):2218–2231. doi: https://doi.org/10.1080/03081087.2017.1391166
- Lin H, Wu B, Chen Y, et al. On the distance and distance Laplacian eigenvalues of graphs. Linear Algebra Appl. 2016;492:128–135. doi: https://doi.org/10.1016/j.laa.2015.11.014
- Lu L, Huang Q, Huang X. On graphs with distance Laplacian spectral radius of multiplicity n−3. Linear Algebra Appl. 2017;530:485–499. doi: https://doi.org/10.1016/j.laa.2017.05.044
- Ma X, Qi L, Tian F, et al. On the distance and distance Laplacian eigenvalues of graphs. Linear Algebra Appl. 2018;557:307–326. doi: https://doi.org/10.1016/j.laa.2018.07.033
- Xue J, Liu S, Shu J. On the multiplicity of distance signless Laplacian eigenvalues of graphs. Linear Multilinear Algebra. 2019 (in press). https://doi.org/https://doi.org/10.1080/03081087.2019.1578726.
- Das KC. On conjectures involving second largest signless Laplacian eigenvalue of graphs. Linear Algebra Appl. 2010;432:3018–3029. doi: https://doi.org/10.1016/j.laa.2010.01.005
- Cvetković D, Simić SK. Towards a spectral theory of graphs based on signless Laplacian I. Publ Inst Math (Beograd). 2009;85(99):19–33. doi: https://doi.org/10.2298/PIM0999019C
- Brouwer AE, Haemers WH. Spectra of graphs. Berlin: Springer; 2011.
- Godsil CD, Royle G. Algebraic graph theory. In: Graduate texts in mathematics. Vol. 207. New York (NY): Springer; 2001.
- Haemers WH. Interlacing eigenvalues and graphs. Linear Algebra Appl. 1995;226–228:593–616. doi: https://doi.org/10.1016/0024-3795(95)00199-2
- Lin H, Zhou B. Graphs with at most one signless Laplacian eigenvalue exceeding three. Linear Multilinear Algebra. 2015;63(2):377–383. doi: https://doi.org/10.1080/03081087.2013.869590
- Stanić Z. On regular graphs and coronas whose second largest eigenvalue does not exceed 1. Linear Multilinear Algebra. 2010;58(5):545–554. doi: https://doi.org/10.1080/03081080802648814