The intersection graph of a finite Moufang loop

The intersection graph ΓSI(G) of a group G with identity element e is the graph whose vertex set is the set V (ΓSI(G)) = G-e and two distinct vertices x and y are adjacent in ΓSI(G) if and only if |⟨x⟩∩⟨y⟩| > 1; where ⟨x⟩ is the cyclic subgroup of G generated by x. In this paper, at first we obtain some results for this graph for any Moufang loop. More specially we observe non-isomorphic finite Moufang loops may have isomorphic intersection graphs.