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|}. In this paper, we study cycle-(super)magic labelings of chain graphs, fans, triangle laders, graphs obtained by joint of a star K1,n with one isolated vertex, laders, and books and P3-(super)magic labelings of cycles. Additionally, we study the dual labeling and present some lower and upper bounds of the magic constant of an H-supermagic labeling.

A graph G is called edge-magic if there exists a bijection f :|} such that f (x) + f (xy) + f (y) is a constant for every edge xy ∈ E(G). A graph G is said to be super edge-magic if f (V (G)) = {1, 2, 3,. .. , |V (G)|}. Furthermore, the edge-magic deficiency of a graph G, µ(G), is defined as the minimum nonnegative integer n such that G∪nK 1 is edge-magic.… (More)

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