Group Distance Magic Labeling of Product of Graphs

Authors

  • Wasim Ashraf Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan.
  • Hani Shaker Department of Mathematics, COMSATS University Islamabad, Lahore Campus, 54000, Pakistan.

Keywords:

Group Distance Magic Labeling, Anti-prism, Cycles, Direct Product

Abstract

A graph is a tool used to build the interconnection network that a system requires. Such networks inter-operability is ensured by specific labeling. There are several labelings in the literature, however the Group Distance Magic Labeling is better for graphs. A graph G is described as ℋ-distance magic graph if for an abelian group ℋ, there exist one-one mapping ???? between group elements and vertex set of graph G such that ⅀ ???? ∈ N(u) ????(x) = µ for all u ∈ V, where µ is the magic constant belongs to abelian group ℋ and N(u) is u′s free neighborhood. In this article, we prove direct product of anti-prism graphs with nth order cycles are ℤ 2st, ℤ2×ℤst, ℤ3 × ℤ2t and ℤ3 × ℤ⅔st distance magic graphs.

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Published

2023-06-30

How to Cite

Group Distance Magic Labeling of Product of Graphs. (2023). Journal of Prime Research in Mathematics, 19(1), 73 – 81. https://jprm.sms.edu.pk/index.php/jprm/article/view/209