On antimagic labeling for generalized web and flower graphs

Abstract

An antimagic labeling of a graph with p vertices and q edges is a bijection from the set of edges to the set of integers { 1, 2, ..., q } such that all vertex weights are pairwise distinct, where a vertex weight is the sum of labels of all edges incident with the vertex. A graph is antimagic if it has an antimagic labeling. Completely separating systems arose from certain problems in information theory and coding theory. Recently these systems have been shown to be useful in constructing antimagic labelings of particular graphs. © 2011 Springer-Verlag.