摘 要：由给定边魔幻图结合群的代数运算系统，构造出奇魔幻群和图-奇魔幻群，得到具有普适性的可算法化的运算方法和简洁明了的结果，给出了互化标号的数学关系式，规模化地构造出方法，构造过程因运算可算法化而得以实施，新定义与算法的引入为不局限于特殊图类标号的研究提供了新的数理支撑。
关键词：边魔幻标号；优美标号；奇优美标号；魔幻群；全魔幻图；运算关系
中图分类号：O157.5 文献标识码：A 文章编号：2096-4706（2019）22-0005-04
Study on the Magic of Graph Structure
YAO Ming1，YAO Bing2，3
（1.Lanzhou Petrochemical Polytechnic，Lanzhou 730060，China；2.College of Mathematics and Statistics，Northwest Normal University，Lanzhou 730070，China；3.School of Electronic and Information Engineering，Lanzhou Jiaotong University，Lanzhou 730070，China）
Abstract：Based on the algebraic operation system of the given edges-magical graph and the group，the odd-magical group and the graph odd-magical group are constructed，and the general algorithmic operation method and simple and clear results are obtained. The mathematical relationship of the mutual label is given，and the method is constructed on a large scale. The construction process is implemented due to the algorithmic operation. The introduction of the new definition and algorithm is not limited to the special graph. The research of class label provides a new mathematical support.
Keywords：edge-magical labellings；graceful trees；odd-graceful trees；magical group；total-magical graphs；operation relation
基金项目：国家自然科学基金资助项目（项目编号：61662066，61363060）；甘肃省财政厅专项资金（项目编号：2014-63）。
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作者简介：姚明（1962-），男，汉族，江苏扬州人，教授，本科，研究方向：图的着色和标号及计算优化。