Abstract
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.
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Hegarty, P., Zhelezov, D. (2014). Can connected commuting graphs of finite groups have arbitrarily large diameter?. In: Matoušek, J., Nešetřil, J., Pellegrini, M. (eds) Geometry, Structure and Randomness in Combinatorics. CRM Series, vol 18. Edizioni della Normale, Pisa. https://doi.org/10.1007/978-88-7642-525-7_8
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DOI: https://doi.org/10.1007/978-88-7642-525-7_8
Publisher Name: Edizioni della Normale, Pisa
Print ISBN: 978-88-7642-524-0
Online ISBN: 978-88-7642-525-7
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