New Computational Result on Harmonious Trees

Details New Computational Result on Harmonious Trees New Computational Result on Harmonious Trees

2011-06-17

arxiv.org/abs/1106.3490v1

Computer Science

Discrete Mathematics

5 pages, source code will be online shortly

Scientific paper

Graham and Sloane proposed in 1980 a conjecture stating that every tree has a harmonious labelling, a graph labelling closely related to additive base. Very limited results on this conjecture are known. In this paper, we proposed a computational approach to this conjecture by checking trees with limited size. With a hybrid algorithm, we are able to show that every tree with at most 31 nodes is graceful, extending the best previous result in this direction.

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