# Trees with minimum number of infima closed sets

**Minisymposium:**
COMBINATORICS

**Content:**
A subset $X$ of $V(T)$ is called an infima closed set of a rooted tree $T$ if for any $u,v\in X$ the merging vertex of the paths joining the root of $T$ to $u$ and $v$ is also in $X$. We determine the trees with minimum number of infima closed sets among all rooted trees of fixed order. It is observed that minimal trees can be obtained from a complete binary trees by attaching more leaves to selected vertices that has at most one non-leaf neighbour.