Abstract
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.
