Wiener Indices of Maximal k-Degenerate Graphs

Abstract

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.