OD-characterization of some alternating groups

Let G be a finite group. Moghaddamfar et al. defined prime graph Γ(G) of group G as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p,q are joined by an edge, denoted by p∼q, if there is an element in G of order pq. Assume |G|=pα11⋯pαkk with P1 ⋯ lt;pk and nature numbers αi with i=1,2,⋯,k. For p∈π(G), let the degree of p be deg(p)=|{q∈π(G)∣q∼p}|, and D(G)=(deg(p1),deg(p2),⋯,deg(pk)). Denote by π(G) the set of prime divisor of |G|. Let GK(G) be the graph with vertex set π(G) such that two primes p and q in π(G) are joined by an edge if G has an element of order p⋅q. We set s(G) to denote the number of connected components of the prime graph GK(G). Some authors proved some groups are OD-characterizable with s(G)≥2. Then for s(G)=1, what is the influence of OD on the structure of groups? We knew that the alternating groups Ap+3, where 7≠p∈π(100!), A130 and A140 are OD-characterizable. Therefore, we naturally ask the following question: if s(G)=1, then is there a group OD-characterizable? In this note, we give a characterization of Ap+3 except A10 with s(Ap+3)=1, by OD, which gives a positive answer to Moghaddamfar and Rahbariyan s conjecture.