engleski

Cyclical edge-connectivity of fullerene graphs and $(k, 6)$-cages

It is shown that every fullerene graph G is cyclically 5-edge-connected, i.e., that G cannot be separated into two components, each containing a cycle, by deletion of fewer than five edges. The result is then generalized to the case of (k, 6)-cages, i.e., polyhedral cubic graphs whose faces are only k-gons and hexagons. Certain linear and exponential lower bounds on the number of perfect matchings in such graphs are also established

Fullerene graphs; Fullerenes; Cyclical edge-connectivity; (k; 6)-cages; Perfect matching

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