The celebrated Erd(o)s-Ko-Rado theorem states that given n≥2k,every intersecting k-uni-form hypergraph G on n vertices has at most(n-1k-1)edges.This paper states spectral versions of the Erd(o)s-Ko-Rado theorem:let G be an intersecting k-uniform hypergraph on n vertices with n≥2k.Then,the sharp upper bounds for the spectral radius of Aα(G)and Q*(G)are presented,where Aα(G)= αD(G)+(1-α)A(G)is a convex linear combination of the degree diagonal tensor D(G)and the adjacency tensor A(G)for 0≤α＜1,and Q*(G)is the incidence Q-tensor,respectively.Furthermore,when n＞2k,the extremal hypergraphs which attain the sharp upper bounds are characterized.The proof mainly relies on the Perron-Frobenius theorem for nonnegative tensor and the property of the maximizing connected hypergraphs.
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