Propagating Graceful Graphs and Trees

TL;DR

This paper explores methods to propagate graceful graphs and trees to better understand their adjacency matrices, providing algorithms aimed at advancing the proof of the Graceful Tree Conjecture.

Contribution

It introduces algorithms for propagating graceful graphs and trees, offering new tools to analyze their structural properties in relation to the conjecture.

Findings

Algorithms for propagating graceful graphs and trees

Insights into graph behavior via adjacency matrices

Potential progress towards the Graceful Tree Conjecture

Abstract

In an attempt to prove the Graceful Tree Conjecture, we present two propagation of graphs. The first is to propagate graceful graphs, and the second is to propagate trees from a gracefully labeled tree. The motivation in propagating such graphs is to see how graphs behave in the lens of their adjacency matrices. Thus, we provide the necessary algorithms for the said objectives.