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Orientable Group Distance Magic Labeling of Directed Graphs

Author

Listed:
  • Wasim Ashraf
  • Hani Shaker
  • Muhammad Imran
  • Tabasam Rashid

Abstract

A directed graph G is said to have the orientable group distance magic labeling if there exists an abelian group ℋ and one-one map ℓ from the vertex set of G to the group elements, such that ∑y∈NG+xℓ⟶y−∑y∈NG−xℓ⟶y=μ for all x∈V, where NGx is the open neighborhood of x, and μ∈ℋ is the magic constant; more specifically, such graph is called orientable ℋ-distance magic graph. In this study, we prove directed antiprism graphs are orientable ℤ2n, ℤ2×ℤn, and ℤ3×ℤ6m-distance magic graphs. This study also concludes the orientable group distance magic labeling of direct product of the said directed graphs.

Suggested Citation

  • Wasim Ashraf & Hani Shaker & Muhammad Imran & Tabasam Rashid, 2022. "Orientable Group Distance Magic Labeling of Directed Graphs," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-5, February.
    • Handle: RePEc:hin:jnlmpe:3536356
    DOI: 10.1155/2022/3536356
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