Magic Labeling of Disjoint Union Graphs

Let G be a graph with vertex set V（G）,edge set E（G）and maximum degreeΔrespectively.G is called degree-magic if it admits a labelling of the edges by integers{1,2,...,|E（G）|}such that for any vertex v the sum of the labels of the edges incident with v is equal to1+|E（G）|/2·d（v）,where d（v）is the degree of v.Let f be a proper edge coloring of G such that for each vertex v∈V（G）,|{e:e∈Ev,f（e）≤Δ/2}|=|{e:e∈Ev,f（e）>Δ/2}|,and such an f is called a balanced edge coloring of G.In this paper,we show that if G is a supermagic even graph with a balanced edge coloring and m≥1,then（2m+1）G is a supermagic graph.If G is a d-magic even graph with a balanced edge coloring and n≥2,then n G is a d-magic graph.Results in this paper generalise some known results.