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Let G be a finite group. The prime graph of G is denoted by Γ(G). We prove  that the simple group PSLn(3), where n ≥ 9, is quasirecognizable by prime  graph; i.e., if G is a finite group such that Γ(G) = Γ(PSLn(3)), then G has a  unique nonabelian composition factor isomorphic to PSLn(3). Darafsheh proved  in 2010 that if p > 3 is a prime number, then the projective special linear  group PSLp(3) is at most 2-recognizable by spectrum. As a consequence of our  result we prove that if n ≥ 9, then PSLn(3) is at most 2-recognizable by  spectrum.

On recognition by prime graph of the projective special linear group over GF(3)