Mathematical Programming Models for Graceful Labeling Problem of 2-Regular Graphs

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Salar Rezaei, Mohsen | 2011

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41991 (01)
University: Sharif University of Technology
Department: Industrial Engineering
Advisor(s): Eshghi, Kourosh
Abstract:
An α-labeling of a graph is a special case of graceful labeling which was introduced in the late 1960’s. Despite the large number of papers published on this subject in literature, there are few particular techniques to find labeling of graphs. There are still many open problems on this subject, some of which are well-known in Graph Theory. In this thesis, first we present and solve several new mathematical and constraint programming models to find α-labeling of 2-regular graphs. Then, a comparison between their results is discussed. Since, proposed models can only label small size graphs; a tabu search algorithm for labeling the big size 2-regular graphs has been developed. By labeling different classes of 2-regular graphs using proposed algorithm, the existence and construction of α-labeling of Q(7,4k)for k≥1, has been proved
Keywords:
Graph Labeling ; Graceful Labeling ; Mathematical Programming ; Tabu Search Algorithm ; Alpha Labeling ; Two Regular Craphs ; Constraint Programming

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