Let C be the set of all central points of graph G and G[C] the subgraph of G induced by C. For any graph H, let \(A(H)=\min_{G}\{| V(G)| -| V(H)|: G[C]\cong H\}.\) F. Buckley, Z. Miller and P. J. Slater [J. Graph Theory 5, 427-434 (1981; Zbl 0449.05056)] demonstrated that A(H)\(\neq 1\), A(H)\(\leq 4\), and proposed an unresolved question: Does there exist a graph H with \(A(H)=3?\) In this paper, the author gives an affirmative answer of the question.