Edge-antimagic graphs

Abstract

For a graph G = ( V , E ) , a bijection g from V ( G ) ∪ E ( G ) into { 1 , 2 , … , | V ( G ) | + | E ( G ) | } is called ( a , d ) -edge-antimagic total labeling of G if the edge-weights w ( xy ) = g ( x ) + g ( y ) + g ( xy ) , xy ∈ E ( G ) , form an arithmetic progression starting from a and having common difference d. An ( a , d ) -edge-antimagic total labeling is called super ( a , d ) -edge-antimagic total if g ( V ( G ) ) = { 1 , 2 , … , | V ( G ) | } . We study super ( a , d ) -edge-antimagic properties of certain classes of graphs, including friendship graphs, wheels, fans, complete graphs and complete bipartite graphs.