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Combinatorial Enumeration of Graphs

In: Probability, Combinatorics and Control

Author

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  • Carlos Rodriguez Lucatero

Abstract

In this chapter, I will talk about some of the enumerative combinatorics problems that have interested researchers during the last decades. For some of those enumeration problems, it is possible to obtain closed mathematical expressions, and for some other it is possible to obtain an estimation by the use of asymptotic methods. Some of the methods used in both cases will be covered in this chapter as well as some application of graph enumeration in different fields. An overview about the enumeration of trees will be given as an example of combinatorial problem solved in a closed mathematical form. Similarly, the problem of enumeration of regular graphs will be discussed as an example of combinatorial enumeration for which it is hard to obtain a closed mathematical form solution and apply the asymptotic estimation method used frequently in analytic combinatorics for this end. An example of application of the enumerative combinatorics for obtaining a result of applicability criteria of selection nodes in a virus spreading control problem will be given as well.

Suggested Citation

  • Carlos Rodriguez Lucatero, 2020. "Combinatorial Enumeration of Graphs," Chapters, in: Andrey Kostogryzov & Victor Korolev (ed.), Probability, Combinatorics and Control, IntechOpen.
    • Handle: RePEc:ito:pchaps:202101
    DOI: 10.5772/intechopen.88805
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    More about this item

    Keywords

    combinatorial graph enumeration; generating functions; probability;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General

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