梯子图、棱柱图和广义Pertersen图的全反幻全标号
Totally Antimagic Total labeling of Ladders, Prisms and Generalised Pertersen graphs
摘要：
给定一个图$G$，如果所有的边权（分别为顶点权）是两两不同的，则$G$上的全标号称为边反魔术全标号（分别为顶点反魔术全标号）。如果在$G$上的一个标号同时是边反魔全标号和顶点反魔全标号，则称为全反魔全标号。允许完全反幻全标号的图称为完全反幻全图。本文证明了梯子图、棱柱图和广义Pertersen图是完全反幻全图。我们还证明了完全反幻全图的链图是完全反幻全图。
英文摘要：
Given a graph $G$, a total labeling on $G$ is called edge-antimagic total (respectively, vertex-antimagic total) if all edge-weights (respectively, vertex-weights) are pairwise distinct. If a labeling on $G$ is simultaneously edge-antimagic total and vertex-antimagic total, it is called a totally antimagic total labeling. A graph that admits totally antimagic total labeling is called a totally antimagic total graph. In this paper, we prove that ladders, prisms and generalised Pertersen graphs are totally antimagic total graphs. We also show that the chain graph of totally antimagic total graphs is a totally antimagic total graph.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
