# A combinatorial identity with applications to forest graphs

## TL;DR

This paper presents an elementary proof of a combinatorial identity relevant to graph theory and demonstrates its applications in counting forests with explicit formulas.

## Contribution

It introduces a new combinatorial identity and applies it to derive closed-form enumeration formulas for forests.

## Key findings

- Elementary proof of a combinatorial identity
- Closed-form enumeration formulas for forests
- Applications in graph theory enumeration

## Abstract

We give an elementary proof of an interesting combinatorial identity which is of particular interest in graph theory and its applications. Two applications to enumeration of forests with closed-form expressions are given.