The bounds of the spectral radius of general hypergraphs in terms of clique number

2020/07/27 by Duan, Cunxiang, Wang, Ligong
#05C50 #15A42 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2007.13282

Abstract

The spectral radius (or the signless Laplacian spectral radius) of a general hypergraph is the maximum modulus of the eigenvalues of its adjacency (or its signless Laplacian) tensor. In this paper, we firstly obtain a lower bound of the spectral radius (or the signless Laplacian spectral radius) of general hypergraphs in terms of clique number. Moreover, we present a relation between a homogeneous polynomial and the clique number of general hypergraphs. As an application, we finally obtain an upper bound of the spectral radius of general hypergraphs in terms of clique number.

Related

• Spectral properties of general hypergraphs
• Sharp bounds for ordinary and signless Laplacian spectral radii of uniform hypergraphs
• A homogeneous polynomial associated with general hypergraphs and its applications
• Spectral radius of uniform hypergraphs and degree sequences
• On the α-spectral radius of uniform hypergraphs