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Reachability relations in digraphs
Aleksander Malnič, Dragan Marušič, Norbert Seifter, Primož Šparl, Boris Zgrablić, 2008, original scientific article

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
Published in RUP: 02.04.2017; Views: 3111; Downloads: 136
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Addressing the fuzzy front end of innovation in an innovative manner
Katarina Košmrlj Muha, Klemen Širok, Borut Likar, 2015, published scientific conference contribution abstract

Keywords: inoviranje, innovation, front end of innovation, problem and opportunity methods
Published in RUP: 13.10.2015; Views: 2918; Downloads: 84
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