References

  1. Abdian A.Z., Mirafzal S.M. On new classes of multicone graph determined by their spectrums. Alg. Struc. Appl. 2015, 2 (1), 23-34.
  2. Abdian A.Z. Graphs which are determined by their spectrum. Konuralp J. Math. 2016, 4 (2), 34-41.
  3. Abdian A.Z. Two classes of multicone graphs determined by their spectra. J. Math. Ext. 2016, 10 (4), 111-121.
  4. Abdian A.Z. Graphs cospectral with multicone graphs $K_w\bigtriangledown L(P)$. TWMS. J. App. Eng. Math. 2017, 7 (1), 181-187.
  5. Abdian A.Z. The spectral determination of the multicone graphs $K_w\bigtriangledown P$. arXiv:1706.02661
  6. Abdian A.Z., Mirafzal S.M. The spectral characterizations of the connected multicone graphs $K_w\bigtriangledown LHS$ and $K_w\bigtriangledown LGQ$(3,9). Discrete Math. Algorithms Appl. 2018, 10 (2), 1850019. doi: 10.1142/S1793830918500192
  7. Abdian A.Z., Mirafzal S.M. The spectral determinations of the connected multicone graphs $K_w\bigtriangledown mP_{17}$ and $K_w\bigtriangledown mS$. Czechoslovak Math. J. 2018. doi: 10.21136/CMJ.2018.0098-17
  8. Abdian A.Z. The spectral determinations of the multicone graphs $K_w\bigtriangledown mC_n$. arXiv preprint. arXiv:1703.08728.
  9. Abdian A.Z., Beineke Lowell. W., Behmaram A. On the spectral determinations of the connected multicone graphs $ K_r\bigtriangledown sK_t$. arXiv preprint. arXiv:1806.02625.
  10. Abdian A.Z., Behmaram A., Fath-Tabar G.H. Graphs determined by signless Laplacian spectra. arXiv:1806.10004.
  11. Mirafzal S.M., Abdian A.Z. The spectral determinations of some classes of multicone graphs. J. Discrete Math. Sci. Crypt. 2018, 21 (1), 179-189.
  12. Borovićanin B., Petrović M. On the index of cactuses with $n$ vertices. Publ. Inst. Math. (Beograd) (N.S.) 2006, 79 (93), 13-18.
  13. Brouwer A.E., Haemers W.H. Spectra of graphs. In: Axler S., Casacuberta C. (Eds.) Universitext, 1. Springer-Verlag, New York, 2012.
  14. Bu C., Zhou J., Li H., Wang W. Spectral characterizations of the corona of a cycle and two isolated vertices. Graphs Combin. 2014, 30 (5), 1123-1133.
  15. Bu C., Zhou J. Signless Laplacian spectral characterization of the cones over some regular graphs. Linear Algebra Appl. 2012, 436 (9), 3634-3641. doi: 10.1016/j.laa.2011.12.035
  16. Cvetković D., Rowlinson P., Simić S., An introduction to the theory of graph spectra. In: Leary I. (Eds.) London Mathematical Society Student Texts, 75. Cambridge University Press, Cambridge, 2010.
  17. Cvetković D., Rowlinson P., Simić S. Signless Laplacians of finite graphs. Linear Algebra Appl. 2007, 423 (1), 155-171. doi: 10.1016/j.laa.2007.01.009
  18. Cvetković D., Simić S. Towards a spectral theory of graphs based on the signless Laplacian, I. Publ. Inst. Math. (Beograd) (N.S.) 2009, 85 (99), 19-33. doi: 10.2298/PIM0999019C
  19. Cvetković D., Simić S. Towards a spectral theory of graphs based on the signless Laplacian, II. Linear Algebra Appl. 2010, 432 (9), 2257-2272. doi: 10.1016/j.laa.2009.05.020
  20. Cvetković D., Simić S. Towards a spectral theory of graphs based on the signless Laplacian, III.Appl. Anal. Discrete Math. 2010, 4 (1), 156-166. doi: 10.2298/AADM1000001C
  21. Cvetković D., Doob M., Sachs H. Spectra of graphs: theory and applications. J. A. Barth, Heidelberg, 1995.
  22. Das K.C., Liu M. Complete split graph determined by its (signless) Laplacian spectrum. Discrete Appl. Math. 2016, 205, 45-51. doi: 10.1016/j.dam.2016.01.003
  23. Das K.C., Liu M. Kite graphs determined by their spectra. Appl. Math. Comput. 2017, 297, 74-78. doi: 10.1016/j.amc.2016.10.032
  24. Günthard Hs.H., Primas H. Zusammenhang von graphtheorie und mo-theotie von molekeln mit systemen konjugierter bindungen. Helv. Chim. Acta 1956, 39 (6), 1645-1653. doi: 10.1002/hlca.19560390623
  25. Huang S., Zhou J., Bu C. Signless Laplacian spectral characterization of graphs with isolated vertices. Filomat 2016, 30 (14), 3689-3696. doi: 10.2298/FIL1614689H
  26. Liu M. Some graphs determined by their (signless) Laplacian spectra. Czechoslovak Math. J. 2012, 62 (4), 1117-1134. doi: 10.1007/s10587-012-0067-9
  27. Liu M., Shan H., Das K.C. Some graphs determined by their (signless) Laplacian spectra. Linear Algebra Appl. 2014, 449, 154-165. doi: 10.1016/j.laa.2014.02.027
  28. Liu X., Lu P. Signless Laplacian spectral characterization of some joins. Electron. J. Linear Algebra 2015, 30, 443-454. doi: 10.13001/1081-3810.1942
  29. Liu M., Liu B., Wei F. Graphs determined by their (signless) Laplacian spectra. Electron. J. Linear Algebra 2011, 22, 112-124. doi: 10.13001/1081-3810.1428
  30. Xu L.Z., He C.X. On the signless Laplacian spectral determination of the join of regular graphs. Discrete Math. Algorithm. Appl. 2014, 6 (4), 1450050. doi: 10.1142/S1793830914500505
  31. Merris R. Laplacian matrices of graphs: a survey. Linear Algebra Appl. 1994, 197-198, 143-176. doi: 10.1016/0024-3795(94)90486-3
  32. Mirzakhah M., Kiani D. The sun graph is determined by its signless Laplacian spectrum. Electron. J. Linear Algebra 2010, 20, 610-620. doi: 10.13001/1081-3810.1397
  33. Mirafzal S.M., Abdian A.Z. Spectral characterization of new classes of multicone graphs. Stud. Univ. Babeş-Bolyai Math. 2017, 62 (3), 275-286. doi: 10.24193/subbmath.2017.3.01
  34. Omidi G.R., Vatandoost E. Starlike trees with maximum degree 4 are determined by their signless Laplacian spectra. Electron. J. Linear Algebra 2010, 20, 274-290. doi: 10.13001/1081-3810.1373
  35. Radosavljević Z., Rašajski M. A class of reflexive cactuses with four cycles. Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. 2003, 14, 63-84.
  36. van Dam E.R., Haemers W.H. Which graphs are determined by their spectrum? Linear Algebra. Appl. 2003, 373, 241-272. doi: 10.1016/S0024-3795(03)00483-X
  37. van Dam E.R., Haemers W.H. Developments on spectral characterizations of graphs. Discrete Math. 2009, 309 (3), 576-586. doi: 10.1016/j.disc.2008.08.019
  38. Wang J.F., Belardo F., Huang Q.X., Borovićanin B., On the two largest $Q$-eigenvalues of graphs. Discrete Math. 2010, 310 (21), 2858-2866. doi: 10.1016/j.disc.2010.06.030
  39. Wang G., Guo G., Min L. On the signless Laplacian spectral characterization of the line graphs of $T$-shape trees. Czechoslovak Math. J. 2014, 64 (2), 311-325.
  40. Wang J.F., Belardo F., Huang Q.X., Marzi E.M.L. Spectral characterizations of dumbbell graphs. Electron. J. Combin. 2010, 17, $\#$R42.
  41. Zhang Y., Liu X., Zhang B., Yong X. The lollipop graph is determined by its $Q$-spectrum. Discrete Math. 2009, 309 (10), 3364-3369. doi: 10.1016/j.disc.2008.09.052