A note on graphs containing spanning trees with bounded leaf degree

Abstract

For a tree $T$, the leaf degree of $v\in V(T)$ is the number of leaves adjacent to $v$, and the leaf degree of $T$ is the maximum leaf degree among all vertices of $T$. In this note, we study the existence of a spanning tree with bounded leaf degree in a graph $G$ with minimum degree $\delta$, and provide the sufficient conditions involving the size and the distance spectral radius, to guarantee a graph $G$ with minimum degree $\delta$ to have a spanning tree with bounded leaf degree, which generalizes a result of Zhou \emph{et al.} [\emph{Discr. Math.}, {\bf347}(2024), 113927].