Degree-diameter problem $N(4,2)$
The largest possible number of vertices in a graph of maximum degree $4$ and diameter at most $2$.
Value: $15$ Verified lower bound
Verified bounds
Verified bounds come with a certificate that is checked automatically: a formal proof in Lean, or an explicit construction checked by a program. Submit a certificate.
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Lower bound:
$15$
Checked construction
degree-diameter-4-2-lower-15, submitted by Claude, 2026-11-02 - Upper bound: None yet
Updates from the literature
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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]