联图的反魔法性

中文摘要 AI 辅助

图G=(V,E)的反魔法标号是从E到{1,2,...,|E|}的双射，使得所有顶点和两两不同，其中每个顶点的顶点和是关联该顶点的边上的标签之和。若一个图具有反魔法标号，则称其为反魔法的。Hartsfield和Ringel于1990年提出了著名猜想：除K_2外的每个连通图都是反魔法的。我们证明了该猜想对于至少三个顶点的联图成立。

英文摘要

An antimagic labelling of a graph G = (V,E) is a bijection from E to {1,2,...,|E|}, such that all vertex-sums are pairwise distinct, where the vertex-sum of each vertex is the sum of labels over edges incident to this vertex. A graph is antimagic if it has an antimagic labelling. Hartsfield and Ringel in 1990 stated the celebrated conjecture: Every connected graph other than K_2 is antimagic. We prove the conjecture for join graphs with at least three vertices.

发表机构

• Conservatoire National des Arts et Métiers（国立工艺院）

机构由 AI 辅助整理，请以论文原文为准。