New Computational Result on Harmonious Trees
arXiv:1106.3490
Abstract
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.
5 pages, source code of the improved version used in yoyo@home is available at http://rechenkraft.net/yoyo/download/download/tmp/hat/HarmoniousB.cpp