A walk of a graph is a if , implies , and implies . The of a set , denoted by , is formed by and the vertices belonging to some weakly toll walk between two vertices of . Set is if . The of , denote by , is the minimum weakly toll convex set containing . The of is the minimum cardinality of a set such that ; and the of is the minimum cardinality of a set such that . In this work, we show how to compute the weakly toll interval and the weakly toll hull numbers of a graph in polynomial time. In contrast, we show that determining the weakly toll convexity number of a graph (the size of a maximum weakly toll convex set different from ) is -hard.

中文翻译：

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计算弱收费凸性中的外壳数和区间数

图的遍历是一个 if 、 暗示 和 暗示 。集合的 ，由 表示 ，由 和 属于某个弱收费的顶点在 的两个顶点之间行走组成。设置为如果 .的 ，用 表示，是包含 的最小弱收费凸集。 of 是满足以下条件的集合的最小基数：而 of 是满足 的集合的最小基数。在这项工作中，我们展示了如何在多项式时间内计算图的弱收费间隔和弱收费船体数。相反，我们表明确定图的弱收费凸数（不同于 的最大弱收费凸集的大小）是困难的。