Evaluating the Minimum Spanning Trees Using Prim's Algorithm  with Undirected Neutrosophic Graphs

Sukanta Ghadei; Amaresh Chandra Panada; Surapati Pramanik; Nihar Ranjan Panda; Prasanta  Kumar Raut

Authors

Sukanta Ghadei Department of Mathematics, C.V. Raman Global University, Bhubaneswar-752054, Odisha, India.
Amaresh Chandra Panada Department of Mathematics, C.V. Raman Global University, Bhubaneswar-752054, Odisha, India.
Surapati Pramanik Department of Mathematics, Nandalal Ghosh B.T. College, Panpur, Narayanpur, Dist-North 24 Parganas, West Bengal, India, PIN-743126
Nihar Ranjan Panda Department of Medical Research. IMS & SUM Hospital, SOA Deemed to be university, India.
Prasanta Kumar Raut Department of Mathematics, Trident Academy of Technology, Bhubaneswar, Odisha, India.

Keywords:

Minimum Spanning Tree; Neutrosophic Graph; Neutrosophic Number; Prim’s Algorithm; Score Function

Abstract

This research paper presents an innovative approach for determining the minimum
spanning tree (MST) in an undirected neutrosophic graph using Prim's Algorithm,
which is extensively used in addressing network optimization problems. We analyze
the effectiveness of Prim's method for constructing the minimum spanning trees in
undirected neutrosophic networks, where edge weights are denoted by neutrosophic
numbers. Neutrosophic numbers with components reflecting truth, uncertainty, and falsehood provide a more sophisticated method of expressing uncertainty in network
modeling. Here, we use a score function to contrast different NMSTs based on weights
calculated by adding neutrosophic numbers. This method is particularly beneficial for
use in transportation, communication networks, and logistics, where uncertain
properties frequently define network configurations. Numerical illustrations prove the
effectiveness of the proposed method, showing its efficiency in handling neutrosophic
graphs and keeping it computationally feasible. The results indicated that the
suggested Prim's algorithm efficiently produces the minimum spanning trees in
uncertain environments and is advantageous for network design and optimization in
these scenarios.

DOI: 10.5281/zenodo.15272504