Maximizing spectral radii of uniform hypergraphs with few edges

TL;DR

This paper explores the hypergraphs with the highest spectral radii given a fixed number of edges, providing characterizations for various classes such as unicyclic and bicyclic hypergraphs.

Contribution

It introduces new characterizations of hypergraphs with maximum spectral radii within specific classes, including unicyclic and bicyclic hypergraphs, based on their structure.

Findings

Identifies hypergraphs with maximum spectral radii among all uniform hypergraphs with fixed edges.

Provides characterizations for unicyclic hypergraphs with maximum spectral radius.

Extends results to linear and power unicyclic and bicyclic hypergraphs with given girth.

Abstract

In this paper we investigate the hypergraphs whose spectral radii attain the maximum among all uniform hypergraphs with given number of edges. In particular we characterize the hypergraph(s) with maximum spectral radius over all unicyclic hypergraphs, linear or power unicyclic hypergraphs with given girth, linear or power bicyclic hypergraphs, respectively.