Gronau, Hans-Dietrich 1951- VerfasserIn aut Schmidmeier, Markus 1963- VerfasserIn aut text Text gw 2007 monographic XA-DE Rostock University of Rostock, Institute of Mathematics publisher 2007 Rostock Universitätsbibliothek distributor eng

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1 Online-Ressource (15 Seiten) Let K be the complete oriented graph on the finite set of vertices A. A family G = {Ga : a ∈ A} of spanning subgraphs of K is an orthogonal cover provided every arrow of K occurs in exactly one Ga and for every two elements a, b ∈ A, the graphs Ga and Gopb have exactly one arrow in common. Gronau, Grüttmüller, Hartmann, Leck and Leck (2002) have observed that if A has the structure of a finite ring and if f ∈ A is such that both f + 1 and f − 1 are units, then the family, obtained by taking for G0 the multiplication graph of f and for Ga the rotation of G0 by a, defines an orthogonal cover on K. In this manuscript we assume that A is a finite abelian group and proceed to (i) generalize this construction to arbitrary endomorphisms of the underlying group and describe the possible graphs, (ii) introduce a duality on the set of orthogonal covers and (iii) give detailed descriptions of the covers in the case where A is cyclic or elementary abelian.<eng> Open Access Urheberrechtsschutz 1.0 Hans-Dietrich O.F. Gronau and Markus Schmidmeier 510 https://purl.uni-rostock.de/rosdok/id00005832 Rostock : Univ., Fachbereich Mathematik, 2007

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Druck-Ausgabe (DE-627)526195088 Gronau, Hans-Dietrich, 1951 - 07/1 urn:nbn:de:gbv:28-rosdok_id00005832-5 10.18453/rosdok_id00005832 1621468879 rda DE-627 261014 198676804X 20261014T142209.0 Converted from MARCXML to MODS version 3.8 using MARC21slim2MODS3-8_XSLT1-0.xsl (Revision 1.174 20250328) ger