A graph theoretical invariant is any mathematical expression based on the elements of a graph that does not depend on numbering of graph elements. A topological index is the numerical result of any graph invariant. They are numbers calculated from a graph representing a molecule, which does not depend on the numbering of the graph vertices or edges. In this paper, the authors investigate new congruence relations from topological indices. They prove some interesting results in number theory using the techniques of chemical graph theory.