Abstract For a given graph G, the Mostar index Mo(G) is the sum of absolute values of the differences between nu(e) and nv(e) over all edges e = u v of G, where nu(e) and nv(e) are, respectively, the number of vertices of G lying closer to u than to v and the number of vertices of G lying closer to v than to u. The degree sequence of a tree is the sequence of the degrees (in descending order) of the non-leaf vertices. This paper determines those trees with a given degree sequence which have the greatest Mostar index. Consequently, all extremal trees with the greatest Mostar index are obtained in the sets of all trees of order n with the maximum degree, the number of leaves, the independence number and the matching number, respectively. On the other hand, some properties of trees with a given degree sequence which have the least Mostar index are given. We also determine those trees with exactly n − 3 or n − 4 leaves when the degree sequence is given, which have the least Mostar index. At last some numerical results are discussed, in which we calculate the Mostar indices of two sets of molecular graphs: octane isomers and benzenoid hydrocarbons; We compare their Mostar indices with some other distance-based topological indices through their correlations with the chemical properties. The linear model for the Mostar index is better than or as good as the models corresponding to the other distance-based indices.

中文翻译：

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给定度数序列的树的Mostar指数的极值

摘要 对于给定的图 G，Mostar 指数 Mo(G) 是所有边 e = G 的 uv 上 nu(e) 和 nv(e) 之差的绝对值之和，其中 nu(e) 和 nv( e) 分别是 G 的顶点数离 u 比离 v 更近，以及 G 离 v 比离 u 更近的顶点数。一棵树的度数序列是非叶子顶点的度数（降序）序列。本文确定具有给定度数序列的那些具有最大莫斯塔尔指数的树。因此，在所有度数最大、叶子数最大、独立数最大、匹配数最大的n阶树的集合中，得到所有Mostar指数最大的极值树。另一方面，给出了具有最小 Mostar 指数的具有给定度数序列的树的一些性质。当给定度数序列时，我们还确定那些具有恰好 n - 3 或 n - 4 个叶子的树，它们具有最小的莫斯塔尔指数。最后讨论了一些数值结果，其中我们计算了两组分子图的Mostar指数：辛烷异构体和苯系烃；我们通过它们与化学性质的相关性将他们的莫斯塔尔指数与其他一些基于距离的拓扑指数进行比较。莫斯塔尔指数的线性模型优于或与其他基于距离的指数对应的模型一样好。其中我们计算了两组分子图的莫斯塔尔指数：辛烷异构体和苯系烃；我们通过它们与化学性质的相关性将他们的莫斯塔尔指数与其他一些基于距离的拓扑指数进行比较。莫斯塔尔指数的线性模型优于或与其他基于距离的指数对应的模型一样好。其中我们计算了两组分子图的莫斯塔尔指数：辛烷异构体和苯系烃；我们通过它们与化学性质的相关性将他们的莫斯塔尔指数与其他一些基于距离的拓扑指数进行比较。莫斯塔尔指数的线性模型优于或与其他基于距离的指数对应的模型一样好。