2011/06/17 by Wenjie Fang, Fang, Wenjie
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Data Management and Algorithms #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #Graph Labeling and Dimension Problems #cs.DM #math.CO
paper · pdf · doi:10.48550/arxiv.1106.3490
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
openalex publication_date 2011/06/17 · arxiv created 2012/10/31 · arxiv updated 2012/11/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.