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

TL;DR

This paper establishes bounds on the spectral radius of general hypergraphs based on their clique number, linking spectral properties to combinatorial structure.

Contribution

It provides new lower and upper bounds for the spectral radius of hypergraphs in terms of clique number, and relates polynomial properties to clique number.

Findings

Lower bound of spectral radius in terms of clique number

Relation between homogeneous polynomial and clique number

Upper bound of spectral radius based on clique number

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.