The Structure Of Functional Graphs For Functions From A Finite Domain To Itself For Which A Half Iterate Exists

Authors

Paweł Marcin Kozyra, Institute of Mathematics Pedagogical University of KrakowFollow

Abstract

The notion of a replica of a nontrivial in-tree is defined. A result enabling to determine whether an in-tree is a replica of another in-tree employing an injective mapping between some subsets of sources of these in-trees is presented. There are given necessary and sufficient conditions for the existence of a functional square root of a function from a finite set to itself through presenting necessary and sufficient conditions for the existence of a square root of a component of the functional graph for the function and for the existence of a square root of the union of two components of the functional graph for the function containing cycles of the same length using the concept of the replica.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 License.

Recommended Citation

Kozyra, Paweł Marcin (2021) "The Structure Of Functional Graphs For Functions From A Finite Domain To Itself For Which A Half Iterate Exists," Theory and Applications of Graphs: Vol. 8: Iss. 1, Article 8.
DOI: 10.20429/tag.2021.080108
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol8/iss1/8