A note on antimagic labelings of trees

In 1990, Hartsfield and Ringel conjectured “Every tree except K2 is antimagic”, where antimagic means that there is a bijection from E(G) to {1, 2,…, |E(G)} such that at each vertex the weight (sum of the labels of incident edges) is different. We call such a labeling a vertex antimagic edge labeling . As a step towards proving this conjecture, we provide a method whereby, given any degree sequence pertaining to a tree, we can construct an antimagic tree based on this sequence. Furthermore, swapping the roles of edges and vertices with respect to a labeling , we provide a method to construct an edge antimagic vertex labeling for any tree and we consider edge antimagic vertex labeling of graphs in general.