In the associations between entities in a domain model, is the direction of the arrow significant?
The question applies to to 1-1, 1-* & *-*
Yes, the direction of the arrow is significant in some situations:
1-1, not significant, there is not an arrow
1-* indicates which side has many objects for one of the other. For instance, if you have entities Order and OrderItem, the arrow would point to the Order entity, indicating that each Order can have many items but each OrderItem can be on only one Order
*-* Important related to the Navigability property of the association. If the Navigability is only to one side of the association, then the direction of the arrow indicates which side can refer to the other side. If the Navigability is both ways, the direction of the arrow is not important. See the properties of the association for Navigability.