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≥ 2 k+ 2 , we characterize all extremal graphs for the upper bound.
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics