Analyzing single-valued neutrosophic fuzzy graphs through matroid perspectives

Abstract

We hope to present this paper on the emergence of a novel category of matroids derived from single-valued neutrosophic (SVN) fuzzy-graphs. The findings of this study make a substantial contribution to both matroid theory and the field of neutrosophic systems. In this study, we aim to introduce the concept of SVN-matroids and conduct a thorough investigation into their fundamental properties. Additionally, we explore the essential requirements for establishing duality within the realm of matroids formed from neutrosophic fuzzy-networks. This investigation encompasses co-weak isomorphism, weak isomorphism, and isomorphism between two matroids. Furthermore, our research proposes the expansion of other graph products and the creation of a SVN-graph to utilize the Greedy and Kruskal algorithms for determining optimal productivity in an information flow of a single-source network within a SVN-network. The application of neutronosophic graph theory offers a paradigm for addressing optimization problems in chemical graph theory, such as identifying the maximal independent set and a minimum spanning tree. When faced with uncertainty, neutrosophic optimization provides more reliable solutions by considering the uncertainties associated with the objective function or constraints.

Keywords

• SVN-matroid
• Dual-matroid
• Independent set
• Bases
• Isomorphism
• Optimal-network