we prove that all connected graphs with exactly two Laplacian eigenvalues greater than two are determined by their Laplacian spectra.
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references
Cvetkovic D,Doob M,Sachs H.Spectra of Graphs-Theory and Applications[M].Heidelberg-Leipzig:Johan Ambrosius Bart,1995.
Dam van E R,Haemers W H.Which graphs are determined by their spectra?[J].Linear Algebra Appl,2003,373:241-272.
Ma X L,Huang Q X,Liu F J.Spectral characterization of unicyclic graphs whose second largest eigenvalue does not exceed1[J].Linear Algebra Appl,2015,471:587-603.
Ma X L,Wen F.Spectral characterization of graphs with small second largest Laplacian eigenvalue[J].Math Rep,2015,accepted.
Li J X,Guo J M,Shiu W C.On the second largest Laplacian eigenvalues of graphs[J].Linear Algebra Appl,2013,438:2438-2446.
Merris R.Laplacian matrices of graphs:a surver[J].Linear Algebra Appl,1994,197:143-176.
Grone R,Merris R,Sunder V.The Laplacian spectrum of a graph[J].SIAM J Matrix Anal Appl,1990,11:218-238.
Grone R,Merris R.The Laplacian spectrum of a graph II[J].SIAM J Discrete math,1994,7:221-229.
Shen X L,Hou Y P.Some trees are determined by their Laplacian spectra[J].J Nat Sci Hunan Norm Univ(in Chinese),2006,29:21-24.
Zhang X D.Graphs characterized by Laplacian eigenvalues[J].Chin Ann Math(Engl Ser),2004,25B:103-110.
He C X,Shao J Y.On the Laplacian spectral radii of bicyclic graphs[J].Discrete Math,2008,308:5981-5995.