Based on the theory of Branch and Bound in the field of algorithm design and analysis, in this dissertation, an algorithm is designed to search for graph labeling. Combining the computer constructive prove with mathematical prove, three classes of graph labelings: graceful labeling, harmonious labeling and magic labeling are researched, some problems and conjectures have been solved respectively.
This paper has studied the narmonicity of the Crown Qn(2| n) ,and given the necessary condition of the harmonicity for the Crown Qn(2|n). Thus,a kind of feasible scheme about harmonious labeling of Crown Qn (2|n) is given and proved the harmonicity of the Crown Qn (2|n ) when n=4,6,8,10,12,14,16,18.
We not only prove K~(4n)_3 (Windmill graph) and _n+K_3 and _n+(K_4-e) are all strongly harmonious graphs, but also give them the strongly harmonious labeling of graphs. Then, we also prove K_n-e is non-strongly harmonious graph.