| Title: | Reachability relations in digraphs |
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| Authors: | ID Malnič, Aleksander (Author)
ID Marušič, Dragan (Author)
ID Seifter, Norbert (Author)
ID Šparl, Primož (Author)
ID Zgrablić, Boris (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.ejc.2007.11.003
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| Language: | English |
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| Work type: | Not categorized |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | IAM - Andrej Marušič Institute
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| Abstract: | In this paper we study reachability relations on vertices of digraphs, informally defined as follows. First, the weight of a walk is equal to the number of edges traversed in the direction coinciding with their orientation, minus the number of edges traversed in the direction opposite to their orientation. Then, a vertex ▫$u$▫ is ▫$R_k^+$▫-related to a vertex ▫$v$▫ if there exists a 0-weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at u has weight in the interval ▫$[0,k]$▫. Similarly, a vertex ▫$u$▫ is ▫$R_k^-$▫-related to a vertex ▫$v$▫ if there exists a 0-weighted walk from ▫$u$▫ to ▫$v$▫ whose every subwalk starting at ▫$u$▫ has weight in the interval ▫$[-k,0]$▫. For all positive integers ▫$k$▫, the relations ▫$R_k^+$▫ and ▫$R_k^-$▫ are equivalence relations on the vertex set of a given digraph. We prove that, for transitive digraphs, properties of these relations are closely related to other properties such as having property ▫$\mathbb{Z}$▫, the number of ends, growth conditions, and vertex degree. |
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| Keywords: | graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth |
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| Year of publishing: | 2008 |
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| Number of pages: | str. 1566-1581 |
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| Numbering: | Vol. 29, no. 7 |
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| PID: | 20.500.12556/RUP-7717  |
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| ISSN: | 0195-6698 |
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| UDC: | 519.17 |
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| DOI: | 10.1016/j.ejc.2007.11.003 |
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| COBISS.SI-ID: | 2017509 |
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| Publication date in RUP: | 02.04.2017 |
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| Views: | 3087 |
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| Downloads: | 136 |
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