Traceability of locally hamiltonian and locally traceable graphs

If P is a given graph property, we say that a graph G is locally P if 〈N(v)〉 has property P for every v ∈ V (G) where 〈N(v)〉 is the induced graph on the open neighbourhood of the vertex v. Pareek and Skupień (C. M. Pareek and Z. Skupień, On the smallest non-Hamiltonian locally Hamiltonian graph, J. Univ. Kuwait (Sci.), 10:9 17, 1983) posed the following two questions. Question 1 Is 9 the smallest order of a connected nontraceable locally traceable graph? Question 2 Is 14 the smallest order of a connected nontraceable locally hamiltonian graph?