For all n ≥ k ≥ 1, every maximal k-degenerate graph has Wiener index at least n^2 - (k+1)n + k(k+1)/2 and at most sum_{i=0}^{floor((n-2)/k)} C(n-ik,2), and for k-trees with n ≥ 2k+2 the upper bound is attained only by P_n^k.
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Wiener indices of maximal $k$-degenerate graphs
For all n ≥ k ≥ 1, every maximal k-degenerate graph has Wiener index at least n^2 - (k+1)n + k(k+1)/2 and at most sum_{i=0}^{floor((n-2)/k)} C(n-ik,2), and for k-trees with n ≥ 2k+2 the upper bound is attained only by P_n^k.