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Groups and Graphs

  • Andries E. Brouwer
  • Willem H. Haemers
Chapter
Part of the Universitext book series (UTX)

Abstract

Let G be a finite group, H a subgroup, and S a subset of G. We can define a graph Г (G,H,S) by taking as vertices the cosets gH (g ∈ G) and calling g1H and g2H adjacent when \(Hg_2^{-1} g1H \subseteq HSH\). The group G acts as a group of automorphisms on Г(G,H,S) via left multiplication, and this action is transitive. The stabilizer of the vertex H is the subgroup H. A graph Γ (G,H,S) with H = 1 is called a Cayley graph.

Keywords

Abelian Group Conjugacy Class Universal Cover Cayley Graph Irreducible Character 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Andries E. Brouwer and Willem H. Haemers 2012

Authors and Affiliations

  • Andries E. Brouwer
    • 1
  • Willem H. Haemers
    • 2
  1. 1.Department of MathematicsEindhoven University of TechnologyEindhovenThe Netherlands
  2. 2.Department of Econometrics and Operations ResearchTilburg UniversityTilburgThe Netherlands

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