完全圖上的(a, d)-antimagic 圖標號

Abstract

圖標號是將整數分配到一個圖的邊或點。圖標號的發展源起於1967年，由Rosa所提出，在1990年，Hartsfield 和 Ringel 引進了 antimagic graph的概念，而(a, d)-antimagic graph 的觀念則是Bodendiek 和 Walther在1993年引入，詳細的資料可以在[2]中參考。在本篇論文我們探討一些(a, d)-antimagic 圖標號的概念，特別是探討完全圖的(a, d)-antimagic 圖標號。

A graph labeling is an assignment of integers to the vertices or edges, or both, subject to certain conditions. Graph labeling methods was introduced by Rosa in 1967.\nHartsfield and Ringel introduced the concept of an antimagic graph in 1990. The concept of an $(a, d)$-antimagic labelings was introduced by Bodendiek and Walther in 1993. See [2] for further introduction.\nIn this paper, we investigate properties of an $(a, d)$-antimagic graph. In particular, we study the $(a, d)$-antimagic labelings of complete graphs.