In this paper, we obtain some properties of signless Laplacian eigenvalues of general hypergraphs. We give the upper and the lower bound of edge connectivity of general hypergraphs in terms of average degree, minimum degree, the rank and the number of vertices, or analytic connectivity α(G), respectively. We also give the upper bound of analytic connectivity α(G) of general hypergraphs in terms of the degrees of vertices. Finally, we obtain the bounds of the smallest H + -eigenvalue of the normalized Laplacian sub-tensors of general hypergraphs.

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Let λ 1 (G) and q 1 (G) be the spectral radius and the signless Laplacian spectral radius of a kuniform hypergraph G, respectively. In this paper, we give the lower bounds of d − λ 1 (H) and 2d − q 1 (H), where H is a proper subgraph of a f (-edge)-connected d-regular (linear) k-uniform hypergraph. Meanwhile, we also give the lower bounds of 2∆ − q 1 (G) and ∆ − λ 1 (G), where G is a nonregular f (-edge)-connected (linear) k-uniform hypergraph with maximum degree ∆.

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