标题： 解决共享和拓扑索引 显示英文标题

标题： Resolving Share and Topological Index

摘要： 一个分子图 $G$ 的原子 $a$ 唯一地确定（分辨）了 $G$ 的一对原子 $(a_1,a_2)$，如果 $a$ 和 $a_1$ 之间的距离与 $a$ 和 $a_2$ 之间的距离不同。 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. 显示英文摘要

摘要： 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.