单圈图的Steiner Wiener指数的极值问题

Extremal problems for Steiner Wiener index of unicyclic graphs

Wiener指数作为化学图论中的一个重要的化学指标,是连通图的任意两个顶点的距离之和。Steiner Wiener指数是Wiener指数的一种推广形式,定义为所有k个顶点的集合S的Steiner距离的和,其中S的Steiner距离是包含S的最小连通子图的边数。本文研究了具有最小(大)Steiner Wiener指数的单圈图结构。

Wiener index is an important chemical index in chemical graph theory,defined as the sum of distances between all pairs of vertices.A generalization of the Wiener index,called the Steiner Wiener index,takes the sum of the Steiner distances over all sets S of cardinality k.The Steiner distance of vertices in a set S is the minimum size of a connected subgraph that contain these vertices.We consider the extremal problems with respect to the Steiner Wiener index among all unicyclic graphs.