Journal article

On Expansive And Anti-Expansive Tree Maps

Year:

2018

Published in:

Opuscula Mathematica
maps on trees
Markov graphs
Sharkovsky’s theorem

With every self-map on the vertex set of a finite tree one can associate the directed graph of a special type which is called the Markov graph. Expansive and anti-expansive tree maps are two extremal classes of maps with respect to the number of loops in their Markov graphs. In this paper we prove that a tree with at least two vertices has a perfect matching if and only if it admits an expansive cyclic permutation of its vertices. Also, we show that for every tree with at least three vertices there exists an expansive map with a weakly connected (strongly connected provided the tree has a perfect matching) Markov graph as well as anti-expansive map with a strongly connected Markov graph.

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On Strongly Connected Markov Graphs Of Maps On Combinatorial Trees

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2023
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Unique Eccentric Point Graphs And Their Eccentric Digraphs

Publisher: Discrete Mathematics

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

2016
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Markov Graphs Of One–Dimensional Dynamical Systems And Their Discrete Analogues

Publisher: Romanian Journal of Mathematics and Computer Science

Authors: Sergiy Kozerenko

2017
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On The Abstract Properties Of Markov Graphs For Maps On Trees

Publisher: Matematicki Bilten

Authors: Sergiy Kozerenko