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JACIII Vol.27 No.5 pp. 837-847
doi: 10.20965/jaciii.2023.p0837
(2023)

Research Paper:

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Novel Concepts on Domination in Neutrosophic Incidence Graphs with Some Applications

Siti Nurul Fitriah Mohamad*,**, Roslan Hasni**,† ORCID Icon, and Florentin Smarandache*** ORCID Icon

*College of Computing, Informatics and Mathematics, Universiti Teknologi MARA
Machang, Kelantan 18500, Malaysia

**Special Interest Group on Modeling and Data Analytics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu
Kuala Nerus, Terengganu 21030, Malaysia

†Corresponding author

***Mathematics & Science Department, The University of New Mexico
705 Gurley Avenue, Gallup, New Mexico 87301, USA

Received:
October 21, 2022
Accepted:
May 8, 2023
Published:
September 20, 2023
Creative Commons License
Keywords:
dominating set, domination number, neutrosophic graph, single-valued neutrosophic incidence graph
Abstract

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.

Incidence graph

Incidence graph

Cite this article as:
S. Mohamad, R. Hasni, and F. Smarandache, “Novel Concepts on Domination in Neutrosophic Incidence Graphs with Some Applications,” J. Adv. Comput. Intell. Intell. Inform., Vol.27 No.5, pp. 837-847, 2023.
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