A sharp upper bound on the spectral radius of a nonnegative k -uniform tensor and its applications to (directed) hypergraphs

[摘要] In this paper, we obtain a sharp upper bound on the spectral radius of a nonnegative k-uniform tensor and characterize when this bound is achieved. Furthermore, this result deduces the main result in [X. Duan and B. Zhou, Sharp bounds on the spectral radius of a nonnegative matrix, Linear Algebra Appl. 439:2961–2970, 2013] for nonnegative matrices; improves the adjacency spectral radius and signless Laplacian spectral radius of a uniform hypergraph for some known results in [D.M. Chen, Z.B. Chen and X.D. Zhang, Spectral radius of uniform hypergraphs and degree sequences, Front. Math. China 6:1279–1288, 2017]; and presents some new sharp upper bounds for the adjacency spectral radius and signless Laplacian spectral radius of a uniform directed hypergraph. Moreover, a characterization of a strongly connected k-uniform directed hypergraph is obtained.

[学科分类] 电力

[关键词] Uniform tensors;Uniform (directed) hypergraphs;Spectral radius;Adjacency;Signless Laplacian