aspg-21-510-1791468732 20261008141212 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2020 8 1 Muhammad Saqlain Department of Mathematics, Lahore Garrison University, Lahore, Pakistan Florentin Smarandache Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA To deal with fluctations in decision-making, fuzzy / neutrosophic numbers are used. The problem having more fluctuations are difficult to sovle. Thus it is a dire need to define higher order number, also It is a very curious question by researchers all around the world that how octagonal neutrosophic number can be represented and how to be graphed? In this research article, the primarily focused on the representation and graphs of octagonal neutrosophic number. at last, a case study is done using VIKOR method based on octagonal neutrosophic number. These representations will be helpful in multi-criteria decision making problems in the case that there are large number of fluctuations. Finally, concluded the present work with future directions. 2020 19 33 510 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.080102 https://www.americaspg.com/journal/21/article/510 https://www.americaspg.com/storage/3196.pdf