Existence of CND Graphs of Orders 10 Through 17

Determine whether a connected, nontraceable, detour graph exists for each order \(n\) with \(10\leq n\leq17\).

Background

A connected, nontraceable, detour (CND) graph is a connected graph whose detour sequence is constant but whose detour order is strictly smaller than its order. The thesis proves that every CND graph has detour order at least 9, thereby excluding CND graphs of orders below 10, and constructs CND graphs for every order greater than 17. The existence question for the intermediate orders is left unresolved.