Application of Mathematical Programming in Graceful and a-Valuation of Quadratic Graphs

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Amini, Mohammad | 2017

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 49597 (01)
University: Sharif University of Technology
Department: Industrial Engineering
Advisor(s): Eshghi, Kourosh
Abstract:
Graceful and α-valuation are the first labeling methods which was introduce in the late 1960. α-Vaulation of a graph is a special cases of graceful labeling. Despite of 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 research, a new mathematical integer model and two constraint programming models are presented for the graph valuation problem in the case of quadratic graphs. Then, a comparision between their results are discussed. The advantages of this model is linearity, independence from graph structure, and the existence of an objective function. The graph labeling problem is NP-Complete; therefore, ant colony algorithm, genetic algorithm and simulated annealing algorithm are also developed to generate feasible labeling for special classes of graphs. Experimental results on large sizes of graphs from literature show the efficiency of proposed model and approach
Keywords:
Graph Labeling ; Ant Colony Algorithm ; Genetic Algorithm ; Constraint Programming ; Mathematical Programming ; Alpha Labeling ; Meta Heuristic Algorithm

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