@Book{198676804X,
author="Gronau, Hans-Dietrich
and Schmidmeier, Markus",
title="Orthogonal covers by multiplication graphs",
series="Preprints aus dem Institut f{\"u}r Mathematik",
year="2007",
address="Germany; Rostock",
abstract="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, Gr{\"u}ttm{\"u}ller, 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>",
note="Hans-Dietrich O.F. Gronau and Markus Schmidmeier",
doi="10.18453/rosdok_id00005832",
url="https://purl.uni-rostock.de/rosdok/id00005832",
url="https://doi.org/10.18453/rosdok_id00005832",
language="English"
}