Journal article

On The Abstract Properties Of Markov Graphs For Maps On Trees

Year:

2017

Published in:

Matematicki Bilten
dynamical system
Markov graph
isomorphism classes
M-graphs
tournaments

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.

Other publications by

16 publications found

2025
Journal article

Graphs With Odd And Even Distances Between Non‑Cut Vertices

Publisher: Opuscula Mathematica

Authors: Sergiy Kozerenko, Kateryna Antoshyna

2024
Journal article

Dynamical Structure Of Metric And Linear Self‑Maps On Combinatorial Trees

Publisher: Discrete Mathematics Letters

Authors: Sergiy Kozerenko

2023
Journal article

Unique Eccentric Point Graphs And Their Eccentric Digraphs

Publisher: Discrete Mathematics

Authors: Sergiy Kozerenko, Artem Hak, Vladyslav Haponenko, Andrii Serdiuk

2016
Journal article

Markov Graphs Of One–Dimensional Dynamical Systems And Their Discrete Analogues

Publisher: Romanian Journal of Mathematics and Computer Science

Authors: Sergiy Kozerenko

2018
Journal article

On Expansive And Anti‑Expansive Tree Maps

Publisher: Opuscula Mathematica

Authors: Sergiy Kozerenko