https://riverpublishersjournal.com/index.php/JGEU <h1>Journal of Graphic Era University</h1> <p>Published by Graphic Era (Deemed to be University), India</p> <p>The frequency of publication is Bi annual</p> <p><strong><em>Journal of Graphic Era University</em></strong> is an international journal of science and technology which published the articles/review papers/case studies that demonstrate interaction between various disciplines such as electronics engineering, mechanical and automobile engineering, petroleum engineering, computer science &amp; engineering, electrical engineering, civil engineering, management, mathematical sciences, space sciences, allied sciences and humanities, biotechnology and their applications.<br />JGEU is an Open Access Journal, and does not charge readers or their institutions for access to the journal articles. The open access supports the rights of users to read, download, copy, distribute, print, search, or link to the full texts of these articles provided they are properly acknowledged and cited.</p> River Publishers en-US Journal of Graphic Era University 0975-1416 https://riverpublishersjournal.com/index.php/JGEU/article/view/421 <p>Nearest neighbour approach for determination of the minimum travelling salesman tour is a well-documented heuristic for a quick identification of the salesman tour and its associated cost. This heuristic has been used on large sized networks for a quick approximate solution to the travelling salesman problem. For the last several years, an alternative approach to the minimum travelling salesman tour has been developed through the minimum spanning tree (MST). The MST was converted to an index restricted MST (IRMST) and that IRMST was used to find the minimum travelling salesman tour. These two approaches, i.e., the greedy heuristics and the index restricted minimum spanning tree seems to have stronger relations and it is this relationship, which has been explored in this paper. The nearest neighbour approach to find the travelling salesman tour has been modified by incorporating the index balancing theorem. A further modification to this heuristic has been suggested to identify the minimum travelling salesman tour. Many small size problems have been attempted using the heuristic discussed in this paper, and it resulted in an optimal solution but an analytical proof for optimality remains a challenge. This approach further strengthens a natural question about the ‘NP Hard’ category associated with the minimum travelling salesman tour problem.</p> Santosh Kumar OAM Elias Munapo Copyright (c) 2025 2025-06-02 2025-06-02 221–244 221–244 10.13052/jgeu0975-1416.1321