ON THE ABSTRACT PROPERTIES OF MARKOV GRAPHS FOR MAPS ON TREES

Authors

  • Sergiy Kozerenko Taras Shevchenko National University of Kyiv image/svg+xml Author

DOI:

https://doi.org/10.37560/matbil17200022k

Keywords:

dynamics on trees, Markov graphs, tournaments

Abstract

Having a dynamical system on the vertex set of a finite tree, one can construct the corresponding Markov graph which is the digraph that encodes covering relation between edges in a tree. Representatives of isomorphism classes of Markov graphs are called M-graphs. In this paper we prove that the class of M-graphs is closed under several prescribed digraph transformations (such as deletion of a vertex in a digraph or taking the disjoint union of digraphs, for example). We also give a complete list of tournaments which are M-graphs as well as of M-graphs with three vertices.

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Published

2017-01-01

Issue

Vol. 41 No. 2 (2017): 41 (LXVII) 2 (2017)

Section

Articles

License

Copyright (c) 2017 Matematichki Bilten

Creative Commons License

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

How to Cite

[1]
S. Kozerenko, “ON THE ABSTRACT PROPERTIES OF MARKOV GRAPHS FOR MAPS ON TREES”, Mat. Bilt., vol. 41, no. 2, pp. 5–21, Jan. 2017, doi: 10.37560/matbil17200022k.