Geodesic
The fan graph is determined by its signless Laplacian spectrum
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 1, pp. 21-31 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $n\geq 3$.
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 $n\geq 3$.
DOI : 10.21136/CMJ.2019.0159-18
Classification : 05C50, 15A18
Keywords: signless Laplacian spectrum; join graph; graph determined by its spectrum 
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Liu, Muhuo; Yuan, Yuan; Chandra Das, Kinkar. The fan graph is determined by its signless Laplacian spectrum. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 1, pp. 21-31. doi: 10.21136/CMJ.2019.0159-18

[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 | MR | JFM

[2] Cvetković, D., Rowlinson, P., Simić, S. K.: Signless Laplacians of finite graphs. Linear Algebra Appl. 423 (2007), 155-171. | DOI | MR | JFM

[3] Das, K. Ch.: The Laplacian spectrum of a graph. Comput. Math. Appl. 48 (2004), 715-724. | DOI | MR | JFM

[4] Das, K. Ch.: On conjectures involving second largest signless Laplacian eigenvalue of graphs. Linear Algebra Appl. 432 (2010), 3018-3029. | DOI | MR | JFM

[5] Das, K. Ch., Liu, M.: Complete split graph determined by its (signless) Laplacian spectrum. Discrete Appl. Math. 205 (2016), 45-51. | DOI | MR | JFM

[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 | MR | JFM

[7] Haemers, W. H.: Interlacing eigenvalues and graphs. Linear Algebra Appl. 226-228 (1995), 593-616. | DOI | MR | JFM

[8] Liu, M.: Some graphs determined by their (signless) Laplacian spectra. Czech. Math. J. 62 (2012), 1117-1134. | DOI | MR | JFM

[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 | MR | JFM

[11] Dam, E. R. van, Haemers, W. H.: Which graphs are determined by their spectrum?. Linear Algebra Appl. 373 (2003), 241-272. | DOI | MR | JFM

[12] Wang, J., Zhao, H., Huang, Q.: Spectral characterization of multicone graphs. Czech. Math. J. 62 (2012), 117-126. | DOI | MR | JFM

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