Combinatorial Enumeration of Graphs

Carlos Rodriguez Lucatero

A chapter in Probability, Combinatorics and Control from IntechOpen

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.

Keywords: combinatorial graph enumeration; generating functions; probability (search for similar items in EconPapers)
JEL-codes: C60 (search for similar items in EconPapers)
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.intechopen.com/chapters/68889 (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ito:pchaps:202101

DOI: 10.5772/intechopen.88805

Access Statistics for this chapter

More chapters in Chapters from IntechOpen
Bibliographic data for series maintained by Slobodan Momcilovic ().