Novel Concepts on Domination in Neutrosophic Incidence Graphs with Some Applications

• Published in: Journal of Advanced Computational Intelligence and Intelligent Informatics
• Main Author: Fitriah Mohamad S.N.; Hasni R.; Smarandache F.
• Format: Article
• Language: English
• Published: Fuji Technology Press 2023
• Online Access: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85174410190&doi=10.20965%2fjaciii.2023.p0837&partnerID=40&md5=d04e929431de87f6a45dbf43df0646ac

In graph theory, the concept of domination is essential in a variety of domains. It has broad applications in diverse fields such as coding theory, computer network models, and school bus routing and facility location problems. If a fuzzy graph fails to obtain acceptable results, neutrosophic sets and neutrosophic graphs can be used to model uncertainty correlated with indeterminate and inconsistent information in arbitrary real-world scenario. In this study, we consider the concept of domination as it relates to single-valued neutrosophic incidence graphs (SVNIGs). Given the importance of domination and its utilization in numerous fields, we propose the application of dominating sets in SVNIG with valid edges. We present some relevant definitions such as those of valid edges, cardinality, and isolated vertices in SVNIG along with some examples. Furthermore, we also show a few significant sets connected to the dominating set in an SVNIG such as independent and irredundant sets. We also investigate a relationship between the concepts of dominating sets and domination numbers as well as irredundant and independence sets in SVNIGs. Finally, a real-life deployment of domination in SVNIGs is investigated in relation to COVID-19 vaccination locations as a practical application. © 2023 Fuji Technology Press. All rights reserved.