Antimagicness of some families of generalized graphs

Abstract An edge labeling of a graph G = (V, E) is a bijection from the set of edges to the set of integers {1, 2, . . . , |E|}. The weight of a vertex v is the sum of the labels of all the edges incident with v. If the vertex weights are all distinct then we say that the labeling is vertex-antimagic, or simply, antimagic. A graph that admits an antimagic labeling is called an antimagic graph. In this paper, we present a new general method of constructing families of graphs with antimagic labelings. In particular, our method allows us to prove that generalized web graphs and generalized flower graphs are antimagic

Antimagicness of some families of generalized graphs

An edge labeling of a graph <i>G</i> = (<i>V,E</i>) is a bijection from the set of edges to the set of integers {1, 2,..., ∣E∣}. The <i>weight</i> of a vertex <i>v</i> is the sum of the labels of all the edges incident with <i>v</i>. If the vertex weights are all distinct then we say that the labeling is <i>vertex-antimagic</i>, or simply, <i>antimagic</i>. A graph that admits an antimagic labeling is called an <i>antimagic graph</i>. In this paper, we present a new general method of constructing families of graphs with antimagic labelings. In particular, our method allows us to prove that generalized web graphs and generalized flower graphs are antimagic