A graph is maximal k-degenerate if each induced subgraph has a vertex of degree at most k and adding any new edge to the graph violates this condition. In this paper, we provide sharp lower and upper bounds on Wiener indices of maximal k-degenerate graphs of order \(n \ge k \ge 1\). A graph is chordal if every induced cycle in the graph is a triangle and chordal maximal k-degenerate graphs of order \(n \ge k\) are k-trees. For k-trees of order \(n \ge 2k+2\), we characterize all extremal graphs for the upper bound.

中文翻译：

---

极大k-简并图的Wiener指数

的曲线图是最大的k简并如果每个导出子具有至多度的顶点ķ和增加任何新的边缘到图形违反这个条件。在本文中，我们为阶k（n \ ge k \ ge 1 \）的最大k退化图的Wiener指数提供了清晰的上下边界。一个图是弦如果图中的每一个引起的周期是三角形和弦最大ķ -degenerate的顺序图\（N \锗的K \）是ķ -树木。对于阶\（n \ ge 2k + 2 \）的k个树，我们表征了所有极值图的上限。