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On connection between α-labelings and edge-antimagic labelings of disconnected graphs

Abstract:

A labeling of a graph is any map that carries some set of graph elements to numbers (usually to the positive integers). An (a,d)edge antanagic total labeling on a graph with p vertices and q edges is defined as a one-to-one map taking the vertices and edges onto the integers 1,2,...,p + q with the property that the sums of the labels on the edges and the labels of their endpoints form an arithmetic sequence starting from a and having a common difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. We use the connection between α-labelings and edge-antimagic labelings for determining a super (a,d)-edge-antimagic total labelings of disconnected graphs. Copyright © 2012, Charles Babbage Research Centre All rights reserved.