the intersection graph of a finitemoufang 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 |hxi ∩ hyi| > 1, where hxi 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.