SOME PROPERTIES OF THE p-SPECTRAL RADIUS ON TENSORS FOR GENERAL HYPERGRAPHS AND THEIR APPLICATIONS.

Let H = (V,E) be a general hypergraph with rank m and co-rank m_c and A_H be its adjacency tensor, the p-spectral radius ρ(p)(H) of H is defined as ρ(p)(H)=max_x∈S^n-1p xT A_Hx, where S^n-1_p = {x ∈ Rⁿ| x |p=1}. For m = mc and p m, we know that there is a unique positive eigenvector x ∈ S^n-1_p belonging to ρ(p)(H) and ρ(p)(H) can be computed by α -normal labeling method. In this paper, we generalize these properties to the case for m ≠ m_c and some other properties are obtained. At the same time, some applications are also given on the properties attained in this paper. [ABSTRACT FROM AUTHOR]