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 all vertices of G have the same weight. In this paper we study these new labellings with a focus on product graphs.
Bibliographical noteFunding Information:
1 Partially supported by the Polish Ministry of Science and Higher Education. 2 Email: email@example.com 3 Email: firstname.lastname@example.org 4 Email: email@example.com 5 Supported by the Australian Research Council. 6 Email: firstname.lastname@example.org
- Distance antimagic labelling
- Distance magic labelling
- Group labelling