V4- Magic Labelings of Some Shell Related Graphs

For any abelian groupA, a graphG= (V, E) is said to beA-magic if there exists a labeling`:E(G)→A\{0}such that the induced vertex set labeling`+:V(G)→Adefined by`+(v) =∑{`(vu) :vu∈E(G)}is a constant map. A graphG= (V, E) is said to bea-sumAmagic if there there exists ana∈Asuch that`+(v) =afor allv∈V. In particular, ifais the identity element 0, we say thatGis zero-sumAmagic. In this paper we will consider the Klein-four groupV4={0, a, b, c}andinvestigate a class ofV4magic shell related graphs that belongs to the following categories:(i)Va, the class ofa-sumV4magic graphs,(ii)V0, the class of zero-sumV4magic graphs,(iii)Va,0, the class of graphs which are botha-sum and zero -sumV4magic