  The study of the relationship between local and global properties of
mathematical objects has always been a key subject of investigation in
different areas of mathematics. A graph $G$ is called locally linear if the
neighbourhood of every vertex of $G$ induces a path. And $G$ is called locally
hamiltonian (traceable) if the neighbourhood of every vertex of $G$ induces a
hamiltonian (traceable) graph. The local properties of graphs are being studied
extensively. For example, the minimum order of a nonhamiltonian (or
nontraceable) locally hamiltonian (or traceable) graph has been determined. In
this paper, we determine the minimum order of a nonhamiltonian locally linear
graph and the minimum size of a nonhamiltonian locally linear graph of a given
order.
