On the spectral radius of nonregular uniform hypergraphs

TL;DR

This paper investigates bounds on the spectral radius and eigenvalues of connected uniform hypergraphs, extending known graph results to hypergraph spectral theory.

Contribution

It provides new lower bounds for the difference between maximum degree and spectral radius, and for the sum of maximum degree and minimum H-eigenvalue in hypergraphs.

Findings

Lower bounds for Δ - λ in hypergraphs

Lower bounds for Δ + μ in hypergraphs

Extension of graph eigenvalue results to hypergraphs

Abstract

Let $G$ be a connected uniform hypergraphs with maximum degree $\Delta$, spectral radius $\lambda$ and minimum H-eigenvalue $\mu$. In this paper, we give some lower bounds for $\Delta-\lambda$, which extend the result of [S.M. Cioab\u{a}, D.A. Gregory, V. Nikiforov, Extreme eigenvalues of nonregular graphs, J. Combin. Theory, Ser. B 97 (2007) 483-486] to hypergraphs. Applying these bounds, we also obtain a lower bound for $\Delta+\mu$.