Some New Results on Lucky Labeling

Authors

J. Ashwini, School of Mathematics, Madurai Kamaraj University, Madurai, Tamilnadu, India and Department of Mathematics, V.V. Vanniaperumal College for Women, Virudhunagar, Tamilnadu, India.Follow
S.Pethanachi Selvam, Department of Mathematics, The Standard Fireworks Rajaratnam College for Women, Sivakasi, Tamilnadu, India.Follow
R.B. Gnanajothi, Department of Mathematics, V.V. Vanniaperumal College for Women, Virudhunagar, Tamilnadu, India.Follow

Abstract

Czerwi’nski et al. introduced Lucky labeling in 2009 and Akbari et al and A.Nellai Murugan et al studied it further. Czerwi’nski defined Lucky Number of graph as follows: A labeling of vertices of a graph G is called a Lucky labeling if for every pair of adjacent vertices u and v in G where . A graph G may admit any number of lucky labelings. The least integer k for which a graph G has a lucky labeling from the set 1, 2, k is the lucky number of G denoted by η(G). This paper aims to determine the lucky number of Complete graph Kn, Complete bipartite graph Km,n and Complete tripartite graph Kl,m,n. It has also been studied how the lucky number changes while adding a graph G with Kn and deleting an edge e from Kn.

Keywords

Complete graph, Complete Bipartite graph, Complete Tripartite graph, Lucky Labeling, Lucky Number

Article Type

Special Issue Article

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite this Article

Ashwini, J.; Selvam, S.Pethanachi; and Gnanajothi, R.B. (2023) "Some New Results on Lucky Labeling," Baghdad Science Journal: Vol. 20: Iss. 1, Article 50.
DOI: https://doi.org/10.21123/bsj.2023.8569