(α,β)-labelling method for k-uniform hypergraph and its applications

Abstract

The α-normal labelling method, which was introduced by Lu and Man in 2014, is an effective method for comparing the adjacency spectral radii of uniform hypergraphs. Recently, the α spectra of graphs and hypergraphs have attracted much attention from researchers. In this paper, we present a new kind of generalization of α-normal labelling method relating to the α-spectral radius of k-uniform hypergraphs. The effect of several types of graph operations on the α-spectral radius of the hypergraph are studied. As applications, we determine the unique hypergraph with the minimum α-spectral radius among connected k-uniform hypergraphs with given edge number, among c-cyclic hypergraphs with c≥1, respectively, and determine the unique supertree with second minimum α-spectral radius. Furthermore, we extend a recent result obtained by Wang and Yuan on the minimum spectral radius of supertrees with some constraints on maximal degree.