Number of edges in degree-magic graphs

A graph G is called degree-magic if it admits a labelling of the edges by integers 1 , 2 , … , | E ( G ) | such that the sum of the labels of the edges incident with any vertex v is equal to 1 2 ( 1 + | E ( G ) | ) deg ( v ) . Degree-magic graphs extend supermagic regular graphs. In this paper, we present some bounds on the number of edges in degree-magic graphs.