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。
Hartsfield 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.
Hartsfield 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.

[1] N. Hartsfield and G. Ringel. Pearls in Graph Theory, Academic Press, Inc., Boston, 1990 (revised 1994), 108–109.
[2] N. Alon, G. Kaplan, A. lev, Y. Roditty and R. Yuster, Dense graphs are antimagic, J Graph Theory 47 (2004), 297–309.
[3] Z. B. Yilma, Antimagic Properties of Graphs with large Maximum degree, J Graph Theory 72 (2013), 367–373.
[4] D. W. Cranston, Regular bipartite graphs are antimagic, J Graph Theory 60 (2009), 173–182.
[5] Tom Eccles, Graphs of large linear size are antimagic, Journal of Graph Theory 81 (2016), 236-261
[6] Yu‐Chang Liang, Xuding Zhu, Antimagic Labeling of Cubic Graphs, Journal of Graph Theory 75 (2014), 31-36
[7] DW Cranston, YC Liang, X Zhu, Regular graphs of odd degree are antimagic, Journal of Graph Theory 80 (2015), 28-33
[8] K Bérczi, A Bernáth, M Vizer, Regular Graphs are Antimagic, arXiv preprint arXiv:1504.08146, 2015