On the spectral radius of uniform weighted hypergraph

Abstract

Let Q k,n be the set of the connected k-uniform weighted hypergraphs with n vertices, where k, n ≥ 3. For a hypergraph G ∈ Q k,n , let A(G), L(G) and Q(G) be its adjacency tensor, Laplacian tensor and signless Laplacian tensor, respectively. The spectral radii of A(G) and Q(G) are investigated. Some basic properties of the Heigenvalue, the H + -eigenvalue and the H ++ -eigenvalue of A(G), L(G) and Q(G) are presented. Several lower and upper bounds of the H-eigenvalue, the H + -eigenvalue and the H ++ -eigenvalue for A(G), L(G) and Q(G) are established. The largest H + -eigenvalue of L(G) and the smallest H + -eigenvalue of Q(G) are characterized.A relationship among the H-eigenvalues of L(G), Q(G) and A(G) is also given.