On cubic polyhedral graphs with prescribed adjacency properties of their faces Original Research Article

We consider classes of cubic polyhedral graphs whose non-q-gonal faces are adjacent to q-gonal faces only. Structural properties of some classes of such graphs are described. For q = 5 we show that all the graphs in this class are cyclically 4-edge-connected. Some cyclically 4edge-connected and cyclically 5-edge-connected non-Hamiltonian members from this class are presented.