Novel Concepts On Domination In Neutrosophic Incidence Graphs With Some Applications
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Novel Concepts on Domination in Neutrosophic Incidence Graphs with Some Applications
Author: Siti Nurul Fitriah Mohamad
language: en
Publisher: Infinite Study
Release Date: 2023-01-01
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.
A Reconsideration of Advanced Concepts in Neutrosophic Graphs: Smart, Zero Divisor, Layered, Weak, Semi, and Chemical Graphs
One of the most powerful tools in graph theory is the classification of graphs into distinct classes based on shared properties or structural features. Over time, many graph classes have been introduced, each aimed at capturing specific behaviors or characteristics of a graph. Neutrosophic Set Theory, a method for handling uncertainty, extends fuzzy logic by incorporating degrees of truth, indeterminacy, and falsity. Building on this framework, Neutrosophic Graphs [9,84,135] have emerged as significant generalizations of fuzzy graphs. In this paper, we extend several classes of fuzzy graphs to Neutrosophic graphs and analyze their properties.
Neutrosophic Sets and Systems, vol. 78/2025
Author: Florentin Smarandache
language: en
Publisher: Infinite Study
Release Date: 2025-02-15
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation