Abstract
Group labelings of magic and antimagic types are analyzed and relationship between them for the graph and its complement are established. The concept of closed group distance magic labeling is introduced. The existence conditions for $$ {Z}_2^{2m} $$ -distance magic labeling of the graph $$ {C}_4^m $$ are found, and a method for its construction is proposed. The existence conditions for $$ {Z}_2^r $$ -distance magic and antimagic labelings of the Cartesian product of regular graphs are established. The results of group remote magic labeling of the connection of two graphs are obtained.
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