aspg-21-955-1791472315 20261008151155 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2021 17 2 Souhail Dhouib Laboratory OLID, Higher Institute of Industrial Management, University of Sfax, Tunisia Said Broumi Regional Center for the Professions of Education and Training,Casablanca-Settat, Morocco; Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, Casablanca, M. Lathamaheswari Department of Mathematics, Hindustan Institute of Technology & Science, Chennai-603 103, India Travelling salesman problem (TSP) is a prominent computational problem where trail technique is used to calculate all the possible travel and choose the best one. Since there is no branching or back tracking in greedy algorithms, determining the run time is much easier than the existing methods and hence, in this paper, a novel greedy method called Dhouib-Matrix-TSP1 is proposed as the first resolution of TSP to get the optimal solution using single valued trapezoidal neutrosophic numbers with several numerical examples. Also, results have been analyzed with graphical solutions. 2021 144 157 955 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.170205 https://www.americaspg.com/journal/21/article/955 https://www.americaspg.com/storage/61669325944.pdf