Graph-Theoretic Verification of Lucky and Proper Lucky Labeling Invariants

S. Akila Devi; S. Vembu; G. Jasmine; S. Christy Deva Suba

doi:https://doi.org/10.14445/22315373/IJMTT-V72I7P102

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 7 | Year 2026 | Article Id. IJMTT-V72I7P102 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I7P102

Graph-Theoretic Verification of Lucky and Proper Lucky Labeling Invariants

S. Akila Devi, S. Vembu, G. Jasmine, S. Christy Deva Suba

Received	Revised	Accepted	Published
24 May 2026	29 Jun 2026	15 Jul 2026	30 Jul 2026

Citation :

S. Akila Devi, S. Vembu, G. Jasmine, S. Christy Deva Suba, "Graph-Theoretic Verification of Lucky and Proper Lucky Labeling Invariants," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 7, pp. 10-13, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I7P102

Abstract

Lucky labeling is a kind of neighborhood summation graph labeling that has been studied for various classes of graphs extensively. However, relatively few efforts have been made to develop algorithms for the systematic verification of lucky and proper lucky labelings. This paper presents an algorithm for verifying lucky and proper lucky labelings of complete multipartite graphs with up to three partitions. The proposed procedure constructs the graph from the given partition sizes, assigns vertex labels according to the prescribed labeling scheme, computes the corresponding neighborhood sums, and verifies the conditions required for both lucky and proper lucky labelings. An illustrative example is provided to demonstrate the correctness of the algorithm.

Keywords

Lucky Labeling, Proper Lucky Labeling, Complete Multipartite Graph, Vertex Labels, Algorithm.

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