International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/510 2020 2020 Department of Mathematics, Lahore Garrison University, Lahore, Pakistan Muhammad Saqlain Department of Mathematics, University of New Mexico, Gallup, NM 87301, USA Florentin Smarandache 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 2020 19 33 10.54216/IJNS.080102 https://www.americaspg.com/articleinfo/21/show/510