Lobsters with an almost perfect matching are graceful

TL;DR

This paper proves that lobsters with a near-perfect matching are always graceful, contributing to the understanding of graph labelings in combinatorics.

Contribution

It establishes that lobsters with a matching covering all but one vertex are necessarily graceful, advancing the theory of graph labelings.

Findings

Lobsters with a near-perfect matching are graceful.

The proof confirms the conjecture for this class of graphs.

Enhances understanding of graph labelings in combinatorics.

Abstract

Let $T$ be a lobster with a matching that covers all but one vertex. We show that in this case, $T$ is graceful.