Graph Enumeration

Vivek S. Borkar (), Vladimir Ejov (), Jerzy A. Filar () and Giang T. Nguyen ()
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Vivek S. Borkar: IIT, Powai
Vladimir Ejov: Flinders University
Jerzy A. Filar: Flinders University
Giang T. Nguyen: Université libre de Bruxelles

Chapter Chapter 10 in Hamiltonian Cycle Problem and Markov Chains, 2012, pp 179-192 from Springer

Abstract: 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.

Keywords: Markov Chain; Operation Research; Travel Salesman Problem; Regular Graph; Markov Decision Process (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-3232-6_10

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