A complete proof of The Graceful Tree Conjecture using the concept of Edge Degree

TL;DR

This paper proves the long-standing Graceful Tree Conjecture by introducing the concept of Edge Degree, providing a complete and rigorous mathematical proof.

Contribution

The paper presents a complete proof of the Graceful Tree Conjecture utilizing the novel concept of Edge Degree, advancing the theoretical understanding of graph labelings.

Findings

Proof confirms all trees are graceful

Introduces Edge Degree as a key concept

Completes the proof of the conjecture

Abstract

We show the Graceful Tree Conjecture holds.