On the Laplacian integral tricyclic graphs |
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Authors: | Xueyi Huang Fei Wen |
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Institution: | College of Mathematics and Systems Science, Xinjiang University, Urumqi, P.R. China. |
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Abstract: | A graph is called Laplacian integral if all its Laplacian eigenvalues are integers. In this paper, we give an edge subdividing theorem for Laplacian eigenvalues of a graph (Theorem 2.1) and characterize a class of k-cyclic graphs whose algebraic connectivity is less than one. Using these results, we determine all the Laplacian integral tricyclic graphs. Furthermore, we show that all the Laplacian integral tricyclic graphs are determined by their Laplacian spectra. |
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Keywords: | Laplacian integral graph algebraic connectivity tricyclic graph |
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