Minimum-Size CND Graphs at Other Orders

Determine for which values of \(n\), besides the exhibited values, there exists a connected, nontraceable, detour graph of order \(n\) and size \(\left\lceil 5n/4\right\rceil\).

Background

The thesis proves the lower bound $|E(G)|\geq\lceil5n/4\rceil$ for CND graphs and constructs examples attaining it for orders $12k$, with $k\geq2$. The unresolved question concerns the other orders for which this lower bound is attainable.