Let F be a simple graph,and Berge F is a hypergraph if each edge of Berge F is obtained by replacing edges in F with hyperedges.Hypergraph is Berge F-free if it does not contain suphypergraph Berge F.The spectral Turan-problem of linear uniform hypergraphs with special structure based on Aα-tensors is studied,and prove the spectral extreme values of Berge C4-free and linear uniform hypergraphs with girth at least 5 respectively.
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