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Graphs determined by their (signless) Laplacian spectra. (English) Zbl 1227.05185

Summary: Let \(S(n, c)= K_1\vee (cK_2\cup(n- 2c- 1)K_1)\), where \(n\geq 2c+ 1\) and \(c\geq 0\). In this paper, \(S(n, c)\) and its complement are shown to be determined by their Laplacian spectra, respectively. Moreover, we also prove that \(S(n, c)\) and its complement are determined by their signless Laplacian spectra, respectively.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
15A18 Eigenvalues, singular values, and eigenvectors
15B36 Matrices of integers
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