Characterization of the group G_2(5) by the prime graph - Darafsheh, M. R.; Nosratpour, P. (Ukrains’kyi Matematychnyi Zhurnal, 2016)
Let G be a finite group. The prime graph of G is a graph Γ (G) with vertex set π (G) and the set of all prime divisors of |G|, where two distinct vertices p and q are adjacent by an edge if G has an element of order pq. We prove that if GΓ (G) = Γ (G_2(5)), then G has a normal subgroup N such that π (N) { 2, 3, 5} and G/N = G_2(5).