• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2022, Volume: 15, Issue: 46, Pages: 2542-2547

Original Article

Lucas Antimagic Labeling of some Star Related Graphs

Received Date:15 September 2022, Accepted Date:25 September 2022, Published Date:10 December 2022


Objective: To identify a new family of Lucas antimagic graph. Methods: A (p;q) graph G is said to be a Lucas antimagic graph if there exists a bijection f : E(G) ! fL1;L2;   Lqg such that the induced injective function f  : V(G) ! f1;2; : : :åLqg given by f  (u) = åe2E(u) f (e) are all distinct (where E(u) is the set of edges incident to u). Findings: In this paper the Lucas Antimagic Labeling of Subdivision of star, Shadow graph of star, Splitting graph of star, Subdivision of Bistar, Shadow graph of Bistar, Splitting graph of Bistar are found. Novelty: It involves the mathematical formulation for labeling the edges of a given graph which in turn gives rise to a new type of labeling called the Lucas antimagic labeling.

Keywords: Subdivision graph; Shadow graph; Splitting graph; Star; Bistar


  1. Gallian JA. A Dynamic Survey of Graph Labeling. The Electronic Journal of Combinatorics. 2022. Available from: http://www.combinatorics.org
  2. Sumathi P, Kumar JS. Fuzzy quotient-3 cordial labeling of star related graphs- Paper I. Malaya Journal of Matematik. 2019;S(1):79–82. Available from: https://doi.org/10.26637/MJM0S01/0020
  3. Ponraj R, Somasndaram S. Pair difference cordiality of Mirror graph, Shadow graph and splitting graph of certain graphs. Maltepe Journal of Mathematics. 2022;4(1):24–32. Available from: https://doi.org/10.47087/mjm.1089672
  4. Chandra B, Kala R. Group S3 cordial prime labeling of some splitting graphs. AIP Conference Proceedings. 2020;2277(1):100009. Available from: https://doi.org/10.1063/5.0025803


© 2022 Sumathi & Chandravadana. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)


Subscribe now for latest articles and news.