Degree-diameter problem $N(4,2)$

The largest possible number of vertices in a graph of maximum degree $4$ and diameter $2$.

Updates

• 1964-11 Lower bound: $15$
  Elspas, B. (1964, November). Topological constraints on interconnection-limited logic. In 1964 Proceedings of the Fifth Annual Symposium on Switching Circuit Theory and Logical Design (pp. 133-137). IEEE.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]
• 1964-11 Upper bound: $15$
  Elspas, B. (1964, November). Topological constraints on interconnection-limited logic. In 1964 Proceedings of the Fifth Annual Symposium on Switching Circuit Theory and Logical Design (pp. 133-137). IEEE.
  [via Table of the largest known graphs of a given diameter and maximal degree - Wikipedia]