On the Diameters of Commuting Graphs Arising from Random Skew-Symmetric Matrices

Hegarty, Peter, 1971 (författare): Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,Chalmers tekniska högskola,Chalmers University of Technology,University of Gothenburg

Zhelezov, Dmitrii, 1987 (författare): Gothenburg University,Göteborgs universitet,Institutionen för matematiska vetenskaper, matematik,Department of Mathematical Sciences, Mathematics,University of Gothenburg,Chalmers tekniska högskola,Chalmers University of Technology

(creator_code:org_t)

2014
2014
Engelska.
Ingår i: Combinatorics, probability & computing. - 0963-5483 .- 1469-2163. ; 23:3, s. 449-459

Relaterad länk:: http://dx.doi.org/10...; visa fler...; https://gup.ub.gu.se...; https://doi.org/10.1...; https://research.cha...; visa färre...

Abstract Ämnesord

Stäng

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. We present heuristic arguments in favour of this conjecture, following the lines of classical arguments for the Erdős–Rényi random graph. 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. Simulations of our model yielded explicit examples of groups whose commuting graphs have all diameters from 2 up to 10.

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