Abstract
A labeling of a graph is a mapping that carries some set of graph elements into numbers (usually positive integers). An ( a , d ) - edge-antimagic total labeling of a graph with p vertices and q edges is a one-to-one mapping that takes the vertices and edges onto the integers 1 , 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 a and having difference d . Such a labeling is called super if the p 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 ) -edge-antimagic total. We also introduce some constructions of non-regular super ( a , 1 ) -edge-antimagic total graphs.
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