V4 Magic Labelings of Some Graphs

LetAbe an abelian group with identity element 0. A graphG= (V, E) is said to admit ana-sumA-magic labeling if there exists an edge labelingℓ:E(G)−→A\{0}anda∈Asuch that theinduced vertex labelingℓ+:V(G)−→Ade ned byℓ+(u) =∑{ℓ(uv) :uv∈E(G)}is the constant map,ℓ+(u) =afor allu∈V(G). Ifa= 0, the labelingℓis called a zero-sumA-magic labeling ofG. A graphGis said to bea-sum (resp.zero-sum)A-magic ifGadmitsana-sum (resp.zero-sum)A-magic labeling. In this paper we will consider the Klein 4 groupV4={0, a, b, c}=Z2⊕Z2and investigate graphs that area-sumA-magic, zero-sumA-magic andbotha-sum and zero-sumA-magic