On the irregularity of uniform hypergraphs

Abstract

For a k-uniform hypergraph G, let β(G)=Δ(G)−ρ(G), where Δ(G) is the maximum degree of G and ρ(G) is the spectral radius of G via its adjacency tensor. This parameter provides a spectral measure for the irregularity of hypergraphs. We study the β-values of k-uniform hypergraphs with given number of edges. For each of the families of hypertrees, non-power hypertrees, and unicyclic hypergraphs, we determine the first few largest β-values and hypergraphs achieving the values.