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A graph G is locally isometric if the subgraph induced by the neighbourhoodof every vertex is an isometric subgraph of G. It is shown that the hamiltoncycle problem for locally isometric graphs with maximum degree at most 8 isNP-complete. Structural characterizations of locally isometric graphs, withmaximum degree at most 6, that are fully cycle extendable, are established andthese results are used to show that locally isometric graphs with maximumdegree at most 6 are weakly pancyclic. This proves Ryjacek's conjecture for asubclass of locally connected graphs.

Global cycle properties in locally isometric graphs