Graph labeling is a versatile tool used across diverse scientific and engineering fields where complex systems are represented as graphs. It provides a structured approach to understand, manipulate, and optimize these systems. By applying graph labeling techniques, researchers and practitioners can analyze signal flow, optimize circuit designs, allocate frequencies in communication networks, model molecular structures in X-ray crystallography, design error-correcting codes in coding theory, plan trajectories in missile guidance systems, and address numerous other challenges in fields ranging from telecommunications to molecular biology. In this paper, we have introduced the L-(3, 2, 1)-labeling index of a graph and obtained bounds for this new parameter.

labeling, L(3, 2, 1)-labeling, degree-index.

Received: March 17, 2025;  Revised: March 21, 2025;  Accepted: May 9, 2025

How to cite this article: Vijayalaxmi S. Shigehalli and Nagaveni Y. Neeralakeri, On L(3, 2, 1)-labeling index of a graph, Advances and Applications in Discrete Mathematics 42(5) (2025), 481-493. https://doi.org/10.17654/0974165825032

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