正則圖的反魔方標法

Abstract

具有m個邊的圖G的反魔方標號，是從E(G)到1,2...m的雙射函數，使得對於所有頂點u和v其標號和彼此相異。\nHartsfield and Ringel猜測每個連通圖，除了K2 以外都有一個反魔方標號，我們證明對於k-正則圖，當k≥2時是正確的。

An antimagic labeling of a graph G with m edges is a bijection from E(G) to 1, 2,..., m such that for all vertices u and v, the sum of labels on edges incident to u differs from edges incident to v.\nHartsfield and Ringel conjectured that every connected graph other than K2 has an antimagic labeling. We prove it is true for k-regular Graph when k≥2.