Wiener-type invariant conditions for k-leaf-connected graphs

For any integer k ? 2, a graph G is called k-leaf-connected if |V(G)| ? k + 1 and given any subset S ? V(G) with |S| = k, G always has a spanning tree T such that S is precisely the set of leaves of T. Obviously, a graph is 2-leaf-connected if and only if it is Hamilton-connected. The Wiener-type invariant o fa c onnectedg raphGa red efineda sfW =u,v?V(G) P ? (Gd (u, v)), where ? (x) is a nonnegative function on the distanceG d (u, v). In this paper, we present best possible Wiener-type invariant conditions to guarantee a graph to be k-leaf-connected, which not only improves the result of Ao et al. (2023), but also extends the result of Zhou et al. (2019). As applications, sufficient conditions for a graph to be k-leaf-connected in terms of the distance (distance signless Laplacian) spectral radius of G are also obtained.