Studies on Lucky Labeling and Network Graph Structures
S. Akila Devi, N. Nagamani, C. Dorathy · JOURNAL OF NOVEL RESEARCH AND INNOVATIVE DEVELOPMENT · 2026
Lucky labeling is an important area in graph labeling that studies the assignment of integer labels to graph vertices such that adjacent vertices obtain distinct neighborhood sums. Over the years, researchers have extended this concept into several variants including proper lucky labeling and d-lucky labeling. These labeling methods have applications in networking, communication systems, coding theory, image processing, and computational biology. This review paper summarizes the development of lucky labeling and discusses major results related to shell graphs, bloom graphs, cubic graphs, proper lucky labeling, and d-lucky labeling. The paper also highlights important theoretical contributions and future directions in graph labeling research.