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Keywords:
signless Laplacian spectrum; join graph; graph determined by its spectrum
Summary:
Given a graph $G$, if there is no nonisomorphic graph $H$ such that $G$ and $H$ have the same signless Laplacian spectra, then we say that $G$ is \hbox {$Q$-DS}. In this paper we show that every fan graph $F_n$ is \hbox {$Q$-DS}, where $F_{n}=K_{1}\vee P_{n-1}$ and $n\geq 3$.
References:
[1] Cvetković, D. M., Doob, M., Gutman, I., Torgašev, A.: Recent Results in the Theory of Graph Spectra. Annals of Discrete Mathematics 36, North-Holland, Amsterdam (1988). DOI 10.1016/S0167-5060(08)70277-2 | MR 0926481 | Zbl 0634.05054
[2] Cvetković, D., Rowlinson, P., Simić, S. K.: Signless Laplacians of finite graphs. Linear Algebra Appl. 423 (2007), 155-171. DOI 10.1016/j.laa.2007.01.009 | MR 2312332 | Zbl 1113.05061
[3] Das, K. Ch.: The Laplacian spectrum of a graph. Comput. Math. Appl. 48 (2004), 715-724. DOI 10.1016/j.camwa.2004.05.005 | MR 2105246 | Zbl 1058.05048
[4] Das, K. Ch.: On conjectures involving second largest signless Laplacian eigenvalue of graphs. Linear Algebra Appl. 432 (2010), 3018-3029. DOI 10.1016/j.laa.2010.01.005 | MR 2639266 | Zbl 1195.05040
[5] Das, K. Ch., Liu, M.: Complete split graph determined by its (signless) Laplacian spectrum. Discrete Appl. Math. 205 (2016), 45-51. DOI 10.1016/j.dam.2016.01.003 | MR 3478617 | Zbl 1333.05180
[6] Freitas, M. A. A. de, Abreu, N. M. M. de, Del-Vecchio, R. R., Jurkiewicz, S.: Infinite families of $Q$-integral graphs. Linear Algebra Appl. 432 (2010), 2352-2360. DOI 10.1016/j.laa.2009.06.029 | MR 2599865 | Zbl 1219.05158
[7] Haemers, W. H.: Interlacing eigenvalues and graphs. Linear Algebra Appl. 226-228 (1995), 593-616. DOI 10.1016/0024-3795(95)00199-2 | MR 1344588 | Zbl 0831.05044
[8] Liu, M.: Some graphs determined by their (signless) Laplacian spectra. Czech. Math. J. 62 (2012), 1117-1134. DOI 10.1007/s10587-012-0067-9 | MR 3010260 | Zbl 1274.05299
[9] Liu, M., Liu, B.: Extremal Theory of Graph Spectrum. Mathematical Chemistry Monographs 22, University of Kragujevac and Faculty of Science Kragujevac, Kragujevac (2018).
[10] Liu, X., Zhang, Y., Gui, X.: The multi-fan graphs are determined by their Laplacian spectra. Discrete Math. 308 (2008), 4267-4271. DOI 10.1016/j.disc.2007.08.002 | MR 2427757 | Zbl 1225.05172
[11] Dam, E. R. van, Haemers, W. H.: Which graphs are determined by their spectrum?. Linear Algebra Appl. 373 (2003), 241-272. DOI 10.1016/S0024-3795(03)00483-X | MR 2022290 | Zbl 1026.05079
[12] Wang, J., Zhao, H., Huang, Q.: Spectral characterization of multicone graphs. Czech. Math. J. 62 (2012), 117-126. DOI 10.1007/s10587-012-0021-x | MR 2899739 | Zbl 1249.05256
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