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Title:Reachability relations, transitive digraphs and groups
Authors:ID Malnič, Aleksander (Author)
ID Potočnik, Primož (Author)
ID Seifter, Norbert (Author)
ID Šparl, Primož (Author)
Files:.pdf RAZ_Malnic_Aleksander_i2015.pdf (311,92 KB)
MD5: 723A914AD0E7AD82996DCF4A48D50154
 
Language:English
Work type:Unknown
Typology:1.01 - Original Scientific Article
Organization:ZUP - University of Primorska Press
Abstract:In [A. Malnič, D. Marušič, N. Seifter, P. Šparl and B. Zgrablič, Reachability relations in digraphs, Europ. J. Combin. 29 (2008), 1566-1581] it was shown that properties of digraphs such as growth, property Z, and number of ends are reflected by the properties of certain reachability relations defined on the vertices of the corresponding digraphs. In this paper we study these relations in connection with certain properties of automorphism groups of transitive digraphs. In particular, one of the main results shows that if atransitive digraph admits a nilpotent subgroup of automorphisms with finitely many orbits, then its nilpotency class and the number of orbits are closely related to particular properties of reachability relations defined on the digraphs in question. The obtained results have interesting implications for Cayley digraphs of certain types of groups such as torsion-free groups of polynomial growth.
Keywords:Cayley digraph, reachability relation
Year of publishing:2015
Number of pages:str. 83-94
Numbering:Vol. 8, no. 1
PID:20.500.12556/RUP-17611 This link opens in a new window
UDC:519.17:512.54
ISSN on article:1855-3966
COBISS.SI-ID:17187161 This link opens in a new window
Publication date in RUP:31.12.2021
Views:1455
Downloads:17
Metadata:XML DC-XML DC-RDF
:
MALNIČ, Aleksander, POTOČNIK, Primož, SEIFTER, Norbert and ŠPARL, Primož, 2015, Reachability relations, transitive digraphs and groups. Ars mathematica contemporanea [online]. 2015. Vol. 8, no. 1, p. 83–94. [Accessed 2 April 2025]. Retrieved from: https://repozitorij.upr.si/IzpisGradiva.php?lang=eng&id=17611
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Record is a part of a journal

Title:Ars mathematica contemporanea
Publisher:Društvo matematikov, fizikov in astronomov, Društvo matematikov, fizikov in astronomov, Univerza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologije
ISSN:1855-3966
COBISS.SI-ID:239049984 This link opens in a new window

Secondary language

Language:Slovenian
Title:Dosegljivostne relacije, tranzitivni digrafi in grupe
Abstract:V [A. Malnič, D. Marušič, N. Seifter, P. Šparl and B. Zgrablič, Reachability relations in digraphs, Europ. J. Combin. 29 (2008), 1566-1581] je bilo pokazano, da se lastnosti usmerjenih grafov, kot so rast, lastnost Z, in število koncev odražajo v lastnostih določenih dosegljivostnih relacij definiranih na vozliščih ustreznih digrafov. V tem članku obravnavamo te relacije v povezavi z določenimi lastnostmi grup avtomorfizmov tranzitivnih digrafov. Posebej, eden od glavnih rezultatov kaže, da če tranzitivni digraf dopušča nilpotentno podgrupo avtomorfizmov s končno mnogo orbitami, potem sta njegov nilpotentni razred in število obit tesno povezana z določenimi lastnostmi dosegljivostnih relacij, definiranih na ustreznih digrafih. Dobljeni rezultati imajo zanimive implikacije za Cayleyeve digrafe določenih tipov grup, kot so grupe brez torzije s polinomsko rastjo.
Keywords:Cayleyjev digraf, dosegljivostna relacija


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