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. Dedicated to Prof. Frank K. Hwang, on the occasion of his 65th birthday. Supported by Faculty Research Grant, Hong Kong Baptist University.