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Applications of mathematical programming in graceful labeling of graphs. (English) Zbl 1073.05063

Summary: Graceful labeling is one of the best known labeling methods of graphs. Despite the large number of papers published on the subject of graph labeling, there are few particular techniques to be used by researchers to gracefully labeled graphs. In this paper, first a new approach based on the mathematical programming technique is presented to model the graceful labeling problem. Then a branching method is developed to solve the problem for special classes of graphs. Computational results show the efficiency of the proposed algorithm for different classes of graphs. One of the interesting results of our model is in the class of trees. The largest tree known to be graceful has at most 27 vertices but our model can easily solve the graceful labeling for trees with 40 vertices.

MSC:

05C78 Graph labelling (graceful graphs, bandwidth, etc.)
90C35 Programming involving graphs or networks
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