A Computational Approach to the Graceful Tree Conjecture

2010/03/15 by Wenjie Fang, Fang, Wenjie · 2 citations
Computer Science · Materials Science · #Graph Labeling and Dimension Problems #Photochromic and Fluorescence Chemistry

paper · pdf · doi:10.48550/arxiv.1003.3045

Abstract

Graceful tree conjecture is a well-known open problem in graph theory. Here we present a computational approach to this conjecture. An algorithm for finding graceful labelling for trees is proposed. With this algorithm, we show that every tree with at most 35 vertices allows a graceful labelling, hence we verify that the graceful tree conjecture is correct for trees with at most 35 vertices.

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• The Graceful Tree Conjecture: a class of graceful diameter-6 trees
• New Computational Result on Harmonious Trees

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