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 at most 6 is known. In the paper we study cyclic 7-edge connectivity of fullerene graphs, distinguishing between degenerate and non-degenerate cyclic edge-cuts, regarding the arrangement of the 12 pentagons. We prove that if there exists a non-degenerate cyclic 7-edge-cut in a fullerene graph, then the graph is a nanotube unless it is one of the two exceptions presented. We determined that there are 57 configurations of degenerate cyclic 7-edge-cuts, and we listed all of them.
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Kardoš, F., Krnc, M., Lužar, B. et al. Cyclic 7-edge-cuts in fullerene graphs. J Math Chem 47, 771–789 (2010) doi:10.1007/s10910-009-9599-0
- Fullerene graph
- Cyclic edge-connectivity
- Cyclic edge-cuts