论文标题
最大化图中拓扑指数的五个结果
Five results on maximizing topological indices in graphs
论文作者
论文摘要
在本文中，我们证明了图形指数的结果集合。我们确定在所有图形中，具有最大的广义维纳指数（例如，超维纳索引）的极端图（例如，给定的匹配数或独立数字）。这概括了Dankelmann的一些工作以及Chung的一些工作。我们还通过从早期的结果中得出了两种恢复结果的替代证明，以最大程度地提高Wiener索引和外部Wiener索引。我们以证明两个猜想结尾。我们证明，如果$ n $至少为$ 9 $，并且通过均衡的完整的双分部分图实现了$ n $至少$ 9 $，则可以通过路径获得偏心的最大差异。
In this paper, we prove a collection of results on graphical indices. We determine the extremal graphs attaining the maximal generalized Wiener index (e.g. the hyper-Wiener index) among all graphs with given matching number or independence number. This generalizes some work of Dankelmann, as well as some work of Chung. We also show alternative proofs for two recents results on maximizing the Wiener index and external Wiener index by deriving it from earlier results. We end with proving two conjectures. We prove that the maximum for the difference of the Wiener index and the eccentricity is attained by the path if the order $n$ is at least $9$ and that the maximum weighted Szeged index of graphs of given order is attained by the balanced complete bipartite graphs.
