The maximum spectral radius of k-uniform hypergraphs with r pendent vertices

Abstract

ABSTRACTLet G be a k-uniform hypergraph. The spectral radius of G is defined as the maximum modulus of eigenvalues of G. In this paper, we characterize the hypergraph on n vertices with maximum spectral radius among all connected k-uniform hypergraphs with exactly r pendent vertices, where or , and establish lower and upper bounds for the maximum spectral radius of connected hypergraphs in terms of the number of pendent vertices when ; We also characterize the unique hypergraphs with maximum spectral radius among all connected k-uniform hypergraphs and supertrees with given number of pendent edges, respectively.