Reachability relations in digraphs
ID Malnič, Aleksander (Avtor), ID Marušič, Dragan (Avtor), ID Seifter, Norbert (Avtor), ID Šparl, Primož (Avtor), ID Zgrablić, Boris (Avtor)

 URL - Predstavitvena datoteka, za dostop obiščite http://dx.doi.org/10.1016/j.ejc.2007.11.003

Izvleček
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.

Jezik: Angleški jezik graph theory, digraph, reachability relations, end of a graph, property ▫$\mathbb{Z}$▫, growth Delo ni kategorizirano (r6) 1.01 - Izvirni znanstveni članek PEF - Pedagoška fakulteta 2008 Str. 1566-1581 Vol. 29, no. 7 20.500.12556/RUL-45605 519.17 0195-6698 10.1016/j.ejc.2007.11.003 2017509 10.07.2015 930 369 AddThis uporablja piškotke, za katere potrebujemo vaše privoljenje.Uredi privoljenje...