The topological index of a graph is a very important topic for chemical graph theory. Many topological indices are defined based on the distance between the vertices and the degree of the vertices. Also, recently some topological indices have been defined based on the neighbour degree of vertices. In 1947, Wiener first time defined a topological index based on the distance between the vertices known as the Wiener index and it is used to find the boiling point of alkanes. This index can determine only for the hydrogen suppress graphs. Latter in 1975, Randic defined a degree-based index which is known as the Randic index and it is useful for non- hydrogen suppress graphs also. Recently, many other topological indices such as Hosoya index, Hyper-Wiener index, Estrada index, Randic index, Zagreb indices, Szeged index, etc. are also defined with several mathematical properties and applications. These indices are used to investigate several physical, chemical and biological properties of chemical graphs. Recently, some of these topological indices have been defined on fuzzy graphs and very few papers have been published on such graphs.