距离是图论学科中最基本的概念之一，关于距离拓扑指标，已经有许多优美、强大的结果。Wiener指标是最早被研究的拓扑指标，Szeged指标是Wiener指标的一种自然推广，距离均衡图与Szeged指标有着密切的关系，也是图论中非常重要的一类图。距离均衡图指标不仅在组合数学中有重要的理论意义，而且在化学图论中有着广泛的实际应用背景。.本项目将研究修正Szeged指标与Wiener指标差值的上界，并刻画达到上界的极图；利用距离均衡图的定义和性质，解决有关（强）距离均衡图的猜想；将经典图论的方法和概率方法相结合，研究距离均衡图与图的其它不变量之间的关系；研究距离均衡图的推广定义。由于距离均衡图指标在社交网络中有着广泛的应用，所以距离均衡图引起了众多研究者的兴趣。

Distance is one of the most basic concepts of graph-theoretic subjects. There are many elegant and powerful results on distance topological index in graph theory. Wiener index is the oldest topological index, Szeged index is an extension of Wiener index, distance-balanced graph, which is also one of the most important graphs, is related to Szeged index. Besides its theoretical interest in combinatorial mathematics, distance-balanced graph also finds practical applications in many problems of chemistry..This project will study the up bounds of the revised Szeged index and the Wiener index and characterize the extremal graphs of the bound. Using the definitions and properties of (strong) distance-balanced graph, we will solve the conjectures of (strong) distance-balanced graph. By combining the classical methods in graph theory and probability method, we will study the relations between distance-balanced graph and other invariants of graph. We will study the generalized definition of distance-balanced graph. Since distance-balanced graph has widely applications in social networks, the study of distance-balanced graph attracts interesting of many researchers.