Cyclic 7-edge-cuts in fullerene graphs

نویسندگان

  • Frantǐsek Kardoš
  • Matjaž Krnc
  • Borut Lužar
  • Riste Škrekovski
چکیده

A fullerene graph is a planar cubic graph whose all faces are pentagonal and hexagonal. The structure of cyclic edge-cuts of fullerene graphs of sizes up to 6 is known. In the paper we study cyclic 7-edge connectivity of fullerene graphs, distinguishing between degenerated and non-degenerated cyclic edge-cuts, regarding the arrangement of the 12 pentagons. We prove that if there exists a non-degenerated cyclic 7-edge-cut in a fullerene graph, then the graph is a nanotube, unless it is one of the two exceptions presented. We also list the configurations of degenerated cyclic 7-edge-cuts. keywords: fullerene, fullerene graph, cyclic edge-connectivity, cyclic edge-cut

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تاریخ انتشار 2009