Group distance magic and antimagic graphs

S. Cichacz, D. Froncek, Kiki Ariyanti, Sanming Zhou

Research output: Contribution to journalArticlepeer-review


Given a graph G with n vertices and an Abelian group A of order n, an A-distance antimagic labelling of G is a bijection from V (G) to A such that the vertices of G have pairwise distinct weights, where the weight of a vertex is the sum (under the operation of A) of the labels assigned to its neighbours. An A-distance magic labelling of G is a bijection from V (G) to A such that the weights of all vertices of G are equal to the same element of A. In this paper we study these new labellings under a general setting with a focus on product graphs. We prove among other things several general results on group antimagic or magic labellings for Cartesian, direct and strong products of graphs. As applications we obtain several families of graphs admitting group distance antimagic or magic labellings with respect to elementary Abelian groups, cyclic groups or direct products of such groups.

Original languageEnglish
Pages (from-to)1159-1176
Number of pages18
JournalActa Mathematica Sinica, English Series
Issue number10
Publication statusPublished - 1 Oct 2016


  • Distance magic labelling
  • distance antimagic labelling
  • group labelling

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