# On the spectral radii of the unicyclic hypergraphs with fixed matching number

## TL;DR

This paper identifies the hypergraphs with the largest spectral radius among connected unicyclic hypergraphs with fixed matching numbers, providing a clear characterization in the context of spectral graph theory.

## Contribution

It determines the unique hypergraphs with maximum spectral radius for unicyclic hypergraphs with given matching numbers, filling a gap in spectral hypergraph theory.

## Key findings

- Identified hypergraphs with maximum spectral radius for fixed matching numbers.
- Characterized the structure of extremal unicyclic hypergraphs.
- Provided proofs for uniqueness of these extremal hypergraphs.

## Abstract

We determine the unique hypergraphs with maximum spectral radius among all connected $k$-uniform ($k\geq 3$) unicyclic hypergraphs with matching number at least $z$, and among all connected $k$-uniform ($k\geq 3$) unicyclic hypergraphs with a given matching number, respectively.