INTEGER-MAGIC SPECTRA OF AMALGAMATIONS OF STARS AND CYCLES
Sin-Min Lee, Ebrahim Salehi · 2003
Abstract. For any positive integer k, a graph G = (V, E) is said to be Zk-magic if there exists a labeling l: E(G) − → Zk − {0} such that the induced vertex set labeling l +: V (G) − → Zk defined by l + (v) = � { l(uv) : uv ∈ E(G)} is a constant map. For a given graph G, the set of all h ∈ Z+ for which G is Zh-magic is called the integer-magic spectrum of G and is denoted by IM(G). In this paper, we will determine the integer-magic spectra of the graphs which are formed by the amalgamation of stars and cycles. In particular, we will provide examples of graphs that for a given n> 2, they are not h-magic for all values of 2 ≤ h ≤ n. 1.