# The reduced formula of the characteristic polynomial of hypergraphs and the spectrum of hyperpaths

## TL;DR

This paper derives a simplified formula for the characteristic polynomial of certain hypergraphs and explicitly determines the eigenvalues of hyperpaths, advancing spectral hypergraph theory.

## Contribution

It introduces a reduced formula for the characteristic polynomial of k-uniform hypergraphs with pendant edges and explicitly computes eigenvalues for hyperpaths.

## Key findings

- Derived a reduced characteristic polynomial formula for hypergraphs with pendant edges.
- Explicitly calculated the eigenvalues of k-uniform hyperpaths.
- Enhanced understanding of spectral properties of hypergraphs.

## Abstract

In this paper, we give a reduced formula of the characteristic polynomial of $k$-uniform hypergraphs with a pendant edge. And the explicit characteristic polynomial and all distinct eigenvalues of $k$-uniform hyperpath are given.