  An atom $a$ of a molecular graph $G$ uniquely determines (resolves) a pair
$(a_1,a_2)$ of atoms of $G$ if the distance between $a$ and $a_1$ is different
from the distance between $a$ and $a_2$. In this paper, we quantify the
involvement of each atom $a$ of $G$ in uniquely determining (resolving) a pair
$(a_1,a_2)$ of atoms of $G$, which is called the resolving share of $a$ for the
pair $(a_1,a_2)$. Using this quantity, we define a distance-based topological
index of a molecular graph, which reflects the topology of that molecular graph
according to the resolvability behavior of each of its atom, and is called the
resolving topological index. Then we compute the resolving topological index of
several molecular graphs.
