Abstarct: In this thesis, some of applications of distance matrix in molecular graphs, are investigated. In this regard, the properties of Wiener index as one of the most important topological indices of molecular graphs baxsed on distance, are studied. Then, topological indices in the discussion of graphs combinations are investigated. In the following, the subject of the fuzzy Wiener index baxsed on fuzzy distance and some of the properties of it are generalized innovative. also some other applications of distance matrix are investigated in graphs.