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Title:Reachability relations in digraphs
Authors:Seifter, Norbert (Author)
Zgrablić, Boris (Author)
Malnič, Aleksander (Author)
Šparl, Primož (Author)
Marušič, Dragan (Author)
Files:URL http://dx.doi.org/10.1016/j.ejc.2007.11.003
 
Language:English
Work type:Not categorized
Tipology:1.01 - Original Scientific Article
Organization:IAM - Andrej Marušič Institute
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.
Keywords:graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth
Year of publishing:2008
Number of pages:str. 1566-1581
Numbering:Vol. 29, no. 7
ISSN:0195-6698
UDC:519.17
COBISS_ID:2017509 Link is opened in a new window
DOI:10.1016/j.ejc.2007.11.003 Link is opened in a new window
Views:894
Downloads:83
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Secondary language

Language:English
Keywords:teorija grafov, usmerjeni grafi, rast

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