On antimagic labeling of regular graphs with particular factors

An antimagic labeling of a finite simple undirected graph with q   edges is a bijection from the set of edges to the set of integers {1,2,…,q}{1,2,…,q} such that the vertex sums are pairwise distinct, where the vertex sum at vertex u   is the sum of labels of all edges incident to such vertex. A graph is called antimagic if it admits an antimagic labeling. It was conjectured by N. Hartsfield and G. Ringel in 1990 that all connected graphs besides K2K2 are antimagic. Another weaker version of the conjecture is every regular graph is antimagic except K2K2. Both conjectures remain unsettled so far. In this article, we focus on antimagic labeling of regular graphs. Certain classes of regular graphs with particular factors are shown to be antimagic. Note that the results here are also valid for regular multi-graphs.