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A graph \(G\) is said to be \emph{hypohamiltonian} if \(G\) is not Hamiltonian but for each \(v \in V(G)\), the vertex-deleted subgraph \(G – v\) is Hamiltonian. In this paper, we show that there is no hypohamiltonian graph on \(17\) vertices and thereby complete the answer to the question, “For which values of \(n\) do there exist hypohamiltonian graphs
on \(n\) vertices?”. In addition, we present an exhaustive list of hypohamiltonian graphs on fewer than \(18\) vertices and extend previously obtained results for cubic hypohamiltonian graphs.