Spectral characterization of graphs whose second largest eigenvalue is less than 1 |
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| Authors: | Fenjin Liu Jianfeng Wang |
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| Institution: | a College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
b Department of Mathematics, Qinghai Normal University, Xining, Qinghai 810008, China |
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| Abstract: | Graphs with second largest eigenvalue λ2?1 are extensively studied, however, whether they are determined by their adjacency spectra or not is less considered. In this paper we completely characterize all the connected bipartite graphs with λ2<1 that are determined by their adjacency spectra. In addition, we prove that all the connected non-bipartite graphs with girth no less than 4 and λ2<1 are determined by their adjacency spectra. |
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| Keywords: | Spectrum Cospectral graphs Second largest eigenvalue Spectral characterization |
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