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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Can connected commuting graphs of finite groups have arbitrarily large diameter?
verfasst von : Peter Hegarty, Dmitry Zhelezov
Erschienen in: Geometry, Structure and Randomness in Combinatorics
Verlag: Scuola Normale Superiore
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We present a two-parameter family, of finite, non-abelian random groups and propose that, for each fixed
k
, as
m
→ ∞ the commuting graph of
G
m,k
is almost surely connected and of diameter
k
. As well as being of independent interest, our groups would, if our conjecture is true, provide a large family of counterexamples to the conjecture of Iranmanesh and Jafarzadeh that the commuting graph of a finite group, if connected, must have a bounded diameter.