Common-center graph property
= Common-center graph property
{title2=$\mathrm{STAR}_n(G)$}
= STAR graph property
{c}
{synonym}
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 $\binom n2$ of edge bits for $n\geq3$.