Abstract
Graph enumeration is a study in graph theory that deals with counting nonisomorphic graphs that have a particular property. Harary and Palmer [58] provide an excellent introduction to the topic of graph enumeration. On counting labeled cubic graphs, there has been a series of results, most notably Read [86], Read [87], Wormald [101], and Wormald [102], which collectively present various approaches for counting labeled cubic graphs, and labeled cubic graphs with a given connectivity. In comparison to labeled cubic graphs, the numeration of unlabeled cubic graphs is a significantly more challenging problem [102]. In 1977, Robinson [88] presented a method to count unlabeled cubic graphs.
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© 2012 Springer Science+Business Media, LLC
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Borkar, V.S., Ejov, V., Filar, J.A., Nguyen, G.T. (2012). Graph Enumeration. In: Hamiltonian Cycle Problem and Markov Chains. International Series in Operations Research & Management Science, vol 171. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3232-6_10
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DOI: https://doi.org/10.1007/978-1-4614-3232-6_10
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