Solving the Minimum Spanning Tree Problem Under Interval-Valued Fermatean Neutrosophic Domain.

In classical graph theory, the minimal spanning tree (MST) is a subgraph that lacks cycles and efficiently connects every vertex by utilizing edges with the minimum weights. The computation of a minimum spanning tree for a graph has been a pervasive problem over time. However, in practical scenarios, uncertainty often arises in the form of fuzzy edge weights, leading to the emergence of the Fuzzy Minimum Spanning Tree (FMST). This specialized approach is adept at managing the inherent uncertainty present in edge weights within a fuzzy graph, a situation commonly encountered in real-world applications. This study introduces the initial optimization approach for the Minimum Spanning Tree Problem within the context of interval-valued fermatean neutrosophic domain. The proposed solution involves the adaptation of the Dhouib-Matrix-MSTP (DM-MSTP) method, an innovative technique designed for optimal resolution. The DM-MSTP method operates by employing a column-row navigation strategy through the adjacency matrix. To the best of our knowledge, instances of this specific problem have not been addressed previously. To address this gap, a case study is generated, providing a comprehensive application of the novel DM-MSTP method with detailed insights into its functionality and efficacy. [ABSTRACT FROM AUTHOR]