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The spectral radius of a uniform hypergraph is defined to be that of theadjacency tensor the hypergraph. It is known that the unique unicyclichypergraph with the largest spectral radius is a nonlinear hypergraph, and theunique linear unicyclic hypergraph with the largest spectral radius is a powerhypergraph. In this paper we determine the the unique linear unicyclichypergraph with the second or third largest spectral radius, where the formerhypergraph is a power hypergraph and the latter hypergraph is a non-powerhypergraph.

The linear unicyclic hypergraph with the second or third largest spectral radius