On Diameters of Cayley Graphs over Matrix Groups
Eitan Porat

TL;DR
This paper proves that for the special linear group over a finite field, large symmetric generating sets have small covering numbers, revealing sharp bounds on the diameters of corresponding Cayley graphs.
Contribution
It establishes sharp bounds on the diameters of Cayley graphs over matrix groups, specifically for SL_n(F_p), with explicit constants and conditions.
Findings
Covering number is at most Cn^2 for large generating sets.
Results are sharp up to the constant C.
Provides bounds on diameters of Cayley graphs over SL_n(F_p).
Abstract
We establish for the matrix group that there exist absolute constants and such that any symmetric generating set , with has a covering number This result is sharp up to the value of the constant .
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Graph theory and applications
