Abstract
The problem of finding the minimum spanning tree (MST) is one of the most studied and important combinatorial optimisation problems in graph theory. Several types of uncertainties exist in real-life problems, which make it very hard to find the exact length of the arc. The neutrosophic set is an efficient tool to model and deal with the uncertainties in information due to inconsistent and indeterminate. In this study, the authors use triangular neutrosophic numbers to represent the edge weights of a neutrosophic graph for the MST problem in the neutrosophic environment. They call this problem a neutrosophic MST (NMST) problem. They formulate the NMST problem in terms of the linear programming model. Here, they introduce an algorithmic method based on a genetic algorithm for solving the NMST problem. They present the utility of triangular neutrosophic numbers as edge weights and their application in the electrical distribution network.
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