Integer-magic spectra of sun graphs

Let A be a non-trivial Abelian group. A graph G=(V,E) is A-magic if there exists a labeling f:E→A \ {0} such that the induced vertex set labeling f ⁺:V→A, defined by f ⁺(v)=∑f(uv) where the sum is over all uv E, is a constant map. The integer-magic spectrum of a graph G is the set IM(G)={k ∈ ℕ | G is ℤ _k -magic}. A sun graph is obtained from an n-cycle, by attaching paths to each pair of adjacent vertices in the cycle. In this paper, we investigate the integer-magic spectra of some sun graphs.