Sufficient conditions for $l$-leaf-connected graphs in terms of the inverse index, the reciprocal product-degree distance, and the multiplicative version of the first Zagreb index

Let $G$ be a graph with at least $l+1$ vertices. If for any subset $S\subseteq V(G)$ with $|S|=l$ there always exists a spanning tree $T$ in $G$ such that $S$ is precisely the set of leaves of $T$, then we say that the graph $G$ is $l$-leaf-connected. Exploring sufficient conditions for graphs that possesses certain properties is a significant and interesting problem in graph theory. In this paper, we present several sufficient conditions in terms of the inverse degree, the reciprocal product-degree distance, and the multiplicative version of the first Zagreb index for a graph to be $l$-leaf-connected.