Signed k-uniform hypergraphs and tensors

Abstract

A signed k-graph is a k-graph with an incidence function on each vertex and its incident edge. In this paper we extend some concepts of the adjacency and Laplacian tensor from k-graphs to signed k-graphs. Based on the spectral properties of the real symmetric tensor, we investigate the H-spectrum of adjacency and Laplacian tensors for signed k-graphs. Finally the inverse Perron value of any vertex is present. Some bounds for the inverse Perron value are established in terms of some invariants including the number of vertices (edges), the degree sequence.