  A graph G is locally isometric if the subgraph induced by the neighbourhood
of every vertex is an isometric subgraph of G. It is shown that the hamilton
cycle problem for locally isometric graphs with maximum degree at most 8 is
NP-complete. Structural characterizations of locally isometric graphs, with
maximum degree at most 6, that are fully cycle extendable, are established and
these results are used to show that locally isometric graphs with maximum
degree at most 6 are weakly pancyclic. This proves Ryjacek's conjecture for a
subclass of locally connected graphs.
