International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/955 2020 2020 Laboratory OLID, Higher Institute of Industrial Management, University of Sfax, Tunisia Souhail Dhouib 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, Morocco Said Broumi Department of Mathematics, Hindustan Institute of Technology & Science, Chennai-603 103, India M. Lathamaheswari 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 2021 144 157 10.54216/IJNS.170205 https://www.americaspg.com/articleinfo/21/show/955