There are many applications of graph theory to a wide variety of subjects which include operation Research, Physics, chemistry, Economics, Genetics, Engineering, computer Science etc.,In a classical graph for each vertex or edge there are two possibilities arises that is either in the graph or not in the graph and this will not classical graph model for uncertain problems. Fuzzy set is a generalized version of the classical set in which objects have different membership degrees between zero and one. More work has already been done on fuzzy graphs. Zadeh introduced the degree of membership/Truth(T) in 1965 and defined the fuzzy set. Atanassov introduced the degree of non-memebership/Falsehood(F) in 1983 and defined the intuitionstic fuzzy set. Smarandache introduced the degree of Indeterminancy/Neutrality(I) as an independent component in 1995 and defined the neutrosophic set on there compenents (T,I,F). Smarandache has introduced in 2020 the n-SuperHyperGraph, with super-vertices that are groups of vertices and hyper-edges defined on power-set of power-set... that is the most general form of graph as today, and n-HyperAlgebra. A SuperHyperGraph, is a HyperGraph (where a group of Edges form a HyperEdge) such that a group of vertices are united all together into a SuperVertex like a group of people (=vertices) that are united all together into an organization (=SuperVertex) ;and further on the n-SuperHyperGraph where many groups (=SuperVertices) are united all together to form a group-of-groups (called 2-SuperVertex, or Type-2 SuperVertex ), then a group of Type-2 SuperVertices forms a Type-3 SuperVertex, . . . , and so on up to Type-n SuperVertex, for any n 1, which better reflects our reality. Later Narmada Devi worked on new type of neutrosophic over,off graph and minimal domination via neutrosophic over graph and neutrosophic over topologized graph. A lot of topological indices are available in chemical-graph theory and H. Wiener proposed the first index to estimate the boiling point of alkanes called ‘Wiener index’. Many topological indices exist only in the crisp but it’s new to the Nover graph environment. The main aim of this paper is to define the topological indices in Nover graphs.