On sufficient conditions for $k$-leaf-connected graphs

Abstract:

      For any integer $k\geq2,$ a graph $G$ is called $k$-leaf-connected if $|V(G)|\geq k+1$ and given any subset $S\subseteq V(G)$ with $|S|=k,$ $G$ always has a spanning tree $T$ such that $S$ is precisely the set of leaves of $T.$ In this paper, we prove best possible sufficient conditions for a graph to be $k$-leaf-connected in terms of the first Zagreb index, second Zagreb index and hyper-Zagreb index of $G$ or its complement.