On super (a,1)(a,1)-edge-antimagic total labelings of regular graphs

A labeling   of a graph is a mapping that carries some set of graph elements into numbers (usually positive integers). An (a,d)(a,d)-edge-antimagic total labeling   of a graph with pp vertices and qq edges is a one-to-one mapping that takes the vertices and edges onto the integers 1,2…,p+q1,2…,p+q, so that the sum of the labels on the edges and the labels of their end vertices forms an arithmetic progression starting at aa and having difference dd. Such a labeling is called super   if the pp smallest possible labels appear at the vertices.In this paper we prove that every even regular graph and every odd regular graph with a 1-factor are super (a,1)(a,1)-edge-antimagic total. We also introduce some constructions of non-regular super (a,1)(a,1)-edge-antimagic total graphs.