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On Super (a,1)-Edge-Antimagic Total Labelings of Regular Graphs
AbstractA 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 sums of the label on the edges and the labels of their end vertices form 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. Status
Accepted for publication in Discrete mathematics (DM).
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