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Isomorphic factorisations VI: Automorphisms

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Combinatorial Mathematics VI

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 748))

Abstract

An isomorphic factorisation of a graph G is a partition of its line set E(G) into isomorphic subgraphs called factor graphs. The question investigated here is how those automorphisms of a complete graph K p which preserve an isomorphic factorisation can act in permuting the factor graphs. The group of these permutations is called the symmetry group. It is clear that the symmetric group S 2 is the only such factor group of degree 2. However, it is shown that all four permutation groups of degree 3 arise from isomorphic factorisations of complete graphs. For E 1 ×S 2 the smallest example requires 10 points. A natural conjecture is that every permutation group of degree d>2 is the symmetry group of an isomorphic factorisation of some complete graph. However no such representation is known for S 6, and it is shown that the representations of S 5 present certain irregularities.

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Authors
  1. R. W. Robinson
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A. F. Horadam W. D. Wallis

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© 1979 Springer-Verlag

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Robinson, R.W. (1979). Isomorphic factorisations VI: Automorphisms. In: Horadam, A.F., Wallis, W.D. (eds) Combinatorial Mathematics VI. Lecture Notes in Mathematics, vol 748. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102691

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  • DOI: https://doi.org/10.1007/BFb0102691

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09555-2

  • Online ISBN: 978-3-540-34857-3

  • eBook Packages: Springer Book Archive

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