A construction of balanced degree-magic graphs

Abstract

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+|E(G)|)deg(v)/2. Degree-magic graphs extend supermagic regular graphs. In this paper, a new construction of balanced degree-magic graphs is introduced.