A stent graft having graft material attached to a stent structure while providing a low profile to the stent graft in its crimped state. The graft material may be attached to an internal surface, an external surface, or both the internal surface and the external surface of the stent. The graft material may cover all or part of such surfaces. The stent graft is expandable upon delivery to the intended treatment site. The expandable nature of the stent graft may be accomplished by self-expanding materials, or through other methods, such as balloon expansion, as generally practiced in the art. The stent graft material is comprised of durable biocompatible materials as generally practiced in the art. The stent graft in its crimped state comprises a low profile fluid flow conduit that is preferably percutaneously delivered, but that may be surgically emplaced to the intended treatment site. Interdigitable stitches on alternating struts of a stent, heat riveted sutures in combination with a preformed hole in a portion of the stent and a washer, or a combination of the interdigitable stitches and the heat riveted sutures and corresponding preformed holes and washers are used to secure the graft material to the stent.