Some properties of Pareto H-eigenvalues on tensors and hypergraphs

A Pareto H-eigenvalue of a tensor A is a real number ? satisfying the complementarity system: 0 ? x ? (Ax-?Ix) ? 0. The Pareto H-spectrum is the set of all Pareto H-eigenvalues. In this note, we first obtain some invariance on Pareto H-spectrum of tensors under tensor permutational similar (resp. diagonal similar) translation. As their application, we know that Pareto H-spectrum of hypergraphs is independent of the ordering of their vertices. Furthermore, we attain some nice properties on Pareto H-spectrum of hypergraphs. At the same time, we improve some results in [4] and [5].