@article{Deng2025, 
author = {Guixin Deng and Li Wang and Caimei Luo},
title = {Group distance magic labeling of the Cartesian product of two directed cycles},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {6},
pages = {4014-4026},
keywords = {group distance magic labeling, magic constant, cartesian product, directed cycles, exponent},
url = {https://www.sciopen.com/article/10.3934/era.2025178},
doi = {10.3934/era.2025178},
abstract = {Let        G    →   be a finite simple directed graph with    n vertices, and let    Γ be a finite abelian group of order    n. A    Γ-distance magic labeling is a bijection    φ  :  V  (      G    →    )  ⟶  Γ for which there exists    c  ∈  Γ such that        ∑          y      ∈              N        +            (      x      )        φ  (  y  )  −      ∑          y      ∈              N        −            (      x      )        φ  (  y  )  =  c for any    x  ∈  V  (      G    →    ), where        N    +    (  x  ) and        N    −    (  x  ) denote the set of the head and the tail of    x, respectively. In this paper, we obtain a necessary and sufficient condition for that there exists a    Γ-distance magic labeling for the Cartesian products of two directed cycles.}
}