Least H-eigenvalue of adjacency tensor of hypergraphs with cut vertices

Let G be a connected hypergraph with even uniformity,which contains cut vertices.Then G is the coalescence of two nontrivial connected sub-hypergraphs(called branches)at a cut vertex.Let A(G)be the adjacency tensor of G.The least H-eigenvalue of A(G)refers to the least real eigenvalue of A(G)associated with a real eigenvector.In this paper,we obtain a perturbation result on the least H-eigenvalue of A(G)when a branch of G attached at one vertex is relocated to another vertex,and characterize the unique hypergraph whose least H-eigenvalue attains the minimum among all hypergraphs in a certain class of hypergraphs which contain a fixed connected hypergraph.