Wiener Indices of Maximal k-Degenerate Graphs

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 >= k >= 1. A graph is chordal if every induced cycle in the graph is a triangle and chordal maximal k-degenerate graphs of order n >= k are k-trees. For k-trees of order n >= 2k + 2, we characterize all extremal graphs for the upper bound.