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On disjoint union of \(\mathrm{M}\)-graphs
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 is...
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/426 |
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| Summary: | 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. |
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