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.