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Paper detail

New Computational Result on Harmonious Trees

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 harmonious, extending the best previous result in this direction.

preprint2012arXivOpen access
Wenjie Fang
math.CODiscrete Mathematics
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Wenjie Fang

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