On the Antimagic Graphs

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Iran Nezhad, Hassan | 2014

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 46058 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Akbari, Saeed
Abstract:
A labeling of a graph is a bijection of edges in graph G to the set {1,2,…, m}. A labeling is antimagic if for any distinct vertices u and v, the sum of the labels on edges incident to u is different from the sum of the labels on edges incident to v. We say a graph is antimagic if it has an antimagic labeling.. In 1990, Hartsfield and Ringel conjectured that every connected graph other than K2 are Antimagic.In this thesis, we show that each graph with at least two degrees can be called Antimagic. We prove this conjecture for regular graphs of odd degree. and then it will be shown that Cartesian graphs have the property of Antimagic Labeling. Finally, we purpose a novel method for k-th powers of cycles
Keywords:
Bipartite Graph ; Antimagic Labeling Graph ; Hall Theorm ; Cartesian Product ; K-Power Cycle