Recent developments with regards to certain open problems in fullerenes and torusenes together with the methods used to solve these problems in a graph-theoretic context are presented. The stability of fullerenes and torusenes via the number of perfect matching and Hamiltonian cycles is considered in more detail.
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Kutnar, K., Marušič, D. (2009). On Certain Graph Theory Applications. In: Naimzada, A.K., Stefani, S., Torriero, A. (eds) Networks, Topology and Dynamics. Lecture Notes in Economics and Mathematical Systems, vol 613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68409-1_15
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