• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2024, Volume: 17, Issue: Special Issue 1, Pages: 93-102

Original Article

Discrete Labeling of Graphs

Received Date:29 August 2023, Accepted Date:05 March 2024, Published Date:31 May 2024


Objectives: To introduce a new type of labeling called Discrete Labeling. This labeling aims at providing the maximum output whenever the inputs are distinct with rational distribution of neighbours thereby exhibiting the stronger form of Cordial labeling. This work serves as an aid in decision-making. Methods: The discrete labels 0 and 1 are cordially assigned to the vertices such that the edges receive labels depending on the incident vertex labels using EX-OR operation with the condition that for every vertex the cardinality of neighbours labeled 0 and 1 differs by at most 1. Findings: This study proposes the discrete labeling of some standard and special graphs. Also it provides the cases for which certain path, star and cycle related graphs admit discrete labeling. Novelty: This labeling uses EX-OR operation which reduces the complexity of having two swords in one sheath. Apart from keeping the distinct vertex labels and edge labels difference minimal, the cardinality of the neighbouring labels of every vertex is also taken into account.

Keywords: Graph Parameters, Discrete, Trees, Cycle, Complete Graphs


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© 2024 Tharani & Saradha. 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)


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