On the Integer-antimagic Spectra of Non-Hamiltonian Graphs

Abstract

Let A be a nontrivial abelian group. A connected simple graph G = ( V, E ) is A antimagic if there exists an edge labeling f : E ( G ) → A \ { 0 } such that the induced vertex labeling f + : V ( G ) → A , defined by f + ( v ) = Σ { f ( u, v ) : ( u, v ) ∈ E ( G ) } , is a one-to-one map. In this paper, we analyze the group-antimagic property for Cartesian products, hexagonal nets and theta graphs.