TheWiener index of unicyclic graphs given number of pendant vertices or cut vertices

摘要

The Wiener index is the sum of distances between all pairs of distinct vertices in a connected graph, which is the oldest topological index related to molecular branching. In this article, we give a condition to determine the graphs having the smallest Wiener index among all unicyclic graphs given number of pendant vertices, and we also determine the graphs having the smallestWiener index among all unicyclic graphs given number of cut vertices.