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Algebra and Discrete Mathematics, 2017, Volume 24, Issue 2, Pages 262–273
(Mi adm632)
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This article is cited in 2 scientific papers (total in 2 papers)
RESEARCH ARTICLE
On disjoint union of $\mathrm{M}$-graphs
Sergiy Kozerenko Faculty of Mechanics and Mathematics, Taras Shevchenko National University of Kyiv, Volodymyrska str., 64, 01033 Kyiv, Ukraine
Abstract:
Given a pair $(X,\sigma)$ consisting of a finite tree $X$ and its vertex self-map $\sigma$ one can construct the corresponding Markov graph $\Gamma(X,\sigma)$ which is a digraph that encodes $\sigma$-covering relation between edges in $X$. $\mathrm{M}$-graphs are Markov graphs up to isomorphism. We obtain several sufficient conditions for the disjoint union of $\mathrm{M}$-graphs to be an $\mathrm{M}$-graph and prove that each weak component of $\mathrm{M}$-graph is an $\mathrm{M}$-graph itself.
Keywords:
tree maps, Markov graphs, Sharkovsky's theorem.
Received: 12.03.2017 Revised: 02.11.2017
Citation:
Sergiy Kozerenko, “On disjoint union of $\mathrm{M}$-graphs”, Algebra Discrete Math., 24:2 (2017), 262–273
Linking options:
https://www.mathnet.ru/eng/adm632 https://www.mathnet.ru/eng/adm/v24/i2/p262
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Abstract page: | 168 | Full-text PDF : | 55 | References: | 27 |
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