Spectral radii of two kinds of uniform hypergraphs

摘要

Let A(H) be the adjacency tensor (hypermatrix) of uniform hypergraph H. The maximum modulus of the eigenvalues of A(H) is called the spectral radius of H, denoted by ρ(H). In this paper, a conjecture concerning the spectral radii of linear bicyclic uniform hypergraphs is solved, with these results the hypergraph with the largest spectral radius is completely determined among the linear bicyclic uniform hypergraphs. For a t-uniform hypergraph G its generalized power r-uniform hypergraph Gr, s is defined in this paper. An exact relation between ρ(G) and ρ(Gr, s) is proved, more precisely ρ(Gr,s)=(ρ(G))tsr.