| Summary: | 碩士 === 大同大學 === 應用數學學系(所) === 97 === Let G=(V,E) be an undirected graph with p vertices and q edges. Let f be a bijection function from E to {1,2,...q}. Then f is an antimagic labeling of G if the induced vertex sum is injective. If G has an antimagic labeling then we say G is antimagic. Furthermore, if there are integers a, d such that f^+ is injective, and f^+(V)={a,a+d,...,a+(p-1)d}, then f is an (a,d)-antimagic labeling of G. If G has an (a,d)-antimagic labeling then we said G is (a,d)-antimagic.
In this thesis, we obtain two results. First, we prove that all Cartesian products of star graphs with star graphs are antimagic for integers m>=n>=3. Finally, we discuss the conjecture that generalized Petersen graph P(n,k) is ((5n+5)/2,2)-antimagic for odd n, n>=5 and 2>=k>=(n-1)/2.
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