G = (V, E)是一圖形， A是一個可交換群。如果存在一個標號 ， 使得對應之頂點集標號 。則稱該圖為A-魔術。其總合全部在上.另我們定義圖形G之集IM(G).
本文所探討的問題為，對給定之圖形G其IM(G)集為何?

Let A be a non-trivial abelian group. A graph G = (V, E) is A-magic if there exists a labeling such that the induced vertex set labeling. The integer-magic spectrum of a graph G is the set IM(G) .
This thesis studies the integer-magic spectrum on several classes of graphs.

Contents

Abstract (Chinese) i
Abstract(English) ii
Contents iii
I. Introduction …1
1.1 Graphs………...1
1.2 Z-magic graphs 3

II. Integer-magic Spectra of Sun Graphs……………4
2.1 Definitions … ……………… …………...4
2.2 Integer-magic spectra of .......7
III. Non -magic Graphs ……..…… 12
3.1 Graphs constructed from sun graphs ……….. ……12
3.2 A conjecture on non Z_k-magic graphs………… ...17
References…………………………………………………………21

Appendix

[1] J. A. Gallian, A dynamic survey of graph labeling, The Electronic Journal of Combinatorics, 5 (2005), #DS6.
[2] W. C. Shiu and Richard M. Low, Integer-magic spectra of sun graphs, to appear.
[3] D. B. West, Introduction to Graph Theory, second edition, Prentice Hall, 2001.