Orthogonal covers by multiplication graphs Gronau, Hans-Dietrich , 1951- (VerfasserIn) Schmidmeier, Markus , 1963- (VerfasserIn) Text Text 2007 2007 eng electronic resourceremoteComputermedienOnline-Ressource1 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 Orthogonal covers by multiplication graphs--(DE-627)526195088 urn:nbn:de:gbv:28-rosdok_id00005832-5 doi: 10.18453/rosdok_id00005832 oclc: 1621468879 ppn: (DE-627)198676804X