On the diameters of McKay graphs for finite simple groups

Martin W. Liebeck, Aner Shalev, Pham Huu Tiep*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


Let G be a finite group, and α a nontrivial character of G. The McKay graph ℳ(G, α) has the irreducible characters of G as vertices, with an edge from χ1 to χ2 if χ2 is a constituent of αχ1. We study the diameters of McKay graphs for simple groups G of Lie type. We show that for any α, the diameter is bounded by a quadratic function of the rank, and obtain much stronger bounds for G = PSLn(q) or PSUn(q).

Original languageAmerican English
Pages (from-to)449-464
Number of pages16
JournalIsrael Journal of Mathematics
Issue number1
StatePublished - Mar 2021

Bibliographical note

Publisher Copyright:
© 2021, The Hebrew University of Jerusalem.


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