 Common-center graph property

All edges of a simple undirected graph have at least one common endpoint. The empty graph is included when there is at least one vertex, and isolated vertices are permitted. This is the star predicate with isolated vertices allowed; a connected star graph is a special case. Its decision-tree depth is the full number $\left(\genfrac{}{}{0ex}{}{n}{2}\right)$ of edge bits for $n\ge 3$.