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Orthomorphism Graphs of Groups

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Book cover Orthogonal Latin Squares Based on Groups

Part of the book series: Developments in Mathematics ((DEVM,volume 57))

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Abstract

In Chapter 1 we defined orthomorphisms and orthogonality of orthomorphisms. As orthogonality is a symmetric relation, we can define and study orthomorphism graphs: graphs whose vertices are orthomorphisms, and in which adjacency implies orthogonality. In this chapter we introduce orthomorphism graphs of groups. We describe the main problems of interest in the study of orthomorphism graphs, and we describe automorphisms and congruences of orthomorphism graphs. We describe some classes of orthomorphism graphs: the orthomorphism graph \(\mathcal {P}(G)\), composed of orthomorphisms of the form x↦xr, orthomorphism graphs derived from difference sets, orthomorphism graphs obtained from automorphisms, and orthomorphism graphs whose vertices are strong complete mappings.

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  1. Mathematics and Statistics, Wright State University, Dayton, OH, USA

    Anthony B. Evans

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Evans, A.B. (2018). Orthomorphism Graphs of Groups. In: Orthogonal Latin Squares Based on Groups. Developments in Mathematics, vol 57. Springer, Cham. https://doi.org/10.1007/978-3-319-94430-2_8

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