McKay trees

Avraham Aizenbud, Inna Entova-Aizenbud

Research output: Contribution to journalArticlepeer-review


Given a finite group G and its representation ρ, the corresponding McKay graph is a graph Γ(G, ρ) whose vertices are the irreducible representations of G; the number of edges between two vertices π, τ of Γ(G, ρ) is dim HomG(π ⊗ ρ, τ). The collection of all McKay graphs for a given group G encodes, in a sense, its character table. Such graphs were also used by McKay to provide a bijection between the finite subgroups of SU(2) and the affine Dynkin diagrams of types A, D, E, the bijection given by considering the appropriate McKay graphs. In this paper, we classify all (undirected) trees which are McKay graphs of finite groups and describe the corresponding pairs (G, ρ); this classification turns out to be very concise. Moreover, we give a partial classification of McKay graphs which are forests, and construct some non-trivial examples of such forests.

Original languageEnglish
Pages (from-to)513-531
Number of pages19
JournalAlgebraic Combinatorics
Issue number2
StatePublished - 1 Jan 2023


  • McKay graphs
  • Representation theory
  • groups

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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