Groups and Graphs

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


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.


Abelian Group Conjugacy Class Universal Cover Cayley Graph Irreducible Character 
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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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