Let N be the set of all positive integers, and Z_n={0, 1, 2, ··· , n —1}. For any h E N, a graph G = (V, E) is said to be Zh-magic if there exists a labeling f : E - Zh {0} such that the induced vertex labeling f~+ :V - Zh, defined by f~+ (v) =Σ_(uvεE) f(uv), is a constant map. The integer-magic spectrum of G is the set IM(G) = {h E N|G is Zh-magic }. A sun graph is obained from attaching a path to each pair of adjacent vertices in an n-cycle. In this paper we showed that the integer-magic spectra of sun graphs are completely determined.Let N be the set of all positive integers, and Z_n={0, 1, 2, ··· , n —1}. For any h E N, a graph G = (V, E) is said to be Zh-magic if there exists a labeling f : E - Zh {0} such that the induced vertex labeling f~+ :V - Zh, defined by f~+ (v) =Σ_(uvεE) f(uv), is a constant map. The integer-magic spectrum of G is the set IM(G) = {h E N|G is Zh-magic }. A sun graph is obained from attaching a path to each pair of adjacent vertices in an n-cycle. In this paper we showed that the integer-magic spectra of sun graphs are completely determined.
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机译：令N为所有正整数的集合，并且Z_n = {0，1，2，...，n_1}。对于任何h EN，如果存在标签f：E-Zh {0}，从而定义了诱导顶点标签f〜+：V-Zh，则图G =（V，E）被称为Zh-magic由f〜+（v）=Σ_（uvεE）f（uv），是一个常数映射。 G的整数魔术光谱是集合IM（G）= {h E N | G是Zh-magic}。通过在n周期中将路径附加到每对相邻顶点，可以得出太阳图。在本文中，我们证明了太阳图的整数魔术光谱是完全确定的。让N为所有正整数的集合，并且Z_n = {0,1,2，···，n -1}。对于任何h EN，如果存在标签f：E-Zh {0}，从而定义了诱导顶点标签f〜+：V-Zh，则图G =（V，E）被称为Zh-magic由f〜+（v）=Σ_（uvεE）f（uv），是一个常数映射。 G的整数魔术光谱是集合IM（G）= {h E N | G是Zh-magic}。通过在n周期中将路径附加到每对相邻顶点，可以得出太阳图。在本文中，我们证明了太阳图的整数魔术光谱是完全确定的。
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