### D4-Magic Graphs

#### Abstract

Consider the set X = {1, 2, 3, 4} with 4 elements. A permutation of X is a function from X to itself that is both one one and on to. The permutations of X with the composition of functions as a binary operation is a nonabelian group, called the symmetric group S 4 . Now consider the collection of all permutations corresponding to the ways that two copies of a square with vertices 1, 2, 3 and 4 can be placed one covering the other with vertices on the top of vertices. This collection form a nonabelian subgroup of S 4 , called the dihedral group D 4 . In this paper, we introduce A-magic labelings of graphs, where A is a finite nonabelian group and investigate graphs that are D 4 -magic. This did not attract much attention in the literature.

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DOI: http://dx.doi.org/10.23755/rm.v42i0.738

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