The Wiener and Terminal Wiener indices of trees

Heydari \cite{heydari2013} presented very nice formulae for the Wiener and terminal Wiener indices of generalized Bethe trees. It is pity that there are some errors for the formulae. In this paper, we correct these errors and characterize all trees with the minimum terminal Wiener index among all the trees of order $n$ and with maximum degree $\Delta$.Comment: 13 page

The extremal values of the Wiener index of a tree with given degree sequence

The Wiener index of a graph is the sum of the distances between all pairs of vertices, it has been one of the main descriptors that correlate achemical compound's molecular graph with experimentally gathered data regarding the compound's characteristics. The tree that minimizes the Wiener index among trees of given maximal degree was studied. We characterize trees that achieve the maximum and minimum Wiener index, given the number of vertices and the degree sequence