Novel Concepts on Domination in Neutrosophic Incidence Graphs with Some Applications

Book excerpt: In graph theory, the concept of domination is essen tial in a variety of domains. It has broad applications in diverse fields such as coding theory, computer net work models, and school bus routing and facility lo cation problems. If a fuzzy graph fails to obtain ac ceptable results, neutrosophic sets and neutrosophic graphs can be used to model uncertainty correlated with indeterminate and inconsistent information in ar bitrary 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 numer ous fields, we propose the application of dominating sets in SVNIG with valid edges. We present some rel evant definitions such as those of valid edges, cardi nality, and isolated vertices in SVNIG along with some examples. Furthermore, we also show a few signifi cant sets connected to the dominating set in an SVNIG such as independent and irredundant sets. We also in vestigate a relationship between the concepts of dom inating sets and domination numbers as well as irre dundant and independence sets in SVNIGs. Finally, a real-life deployment of domination in SVNIGsis inves tigated in relation to COVID-19 vaccination locations as a practical application.