Final answer:
The correct way to assess the patency of a newly placed arteriovenous graft for dialysis is by listening with a stethoscope over the graft for the presence of a bruit.
Step-by-step explanation:
To assess the patency of a newly placed arteriovenous graft for dialysis, the nurse should listen with a stethoscope over the graft for the presence of a bruit. A bruit is a whooshing sound that indicates blood is flowing through the graft, which means the graft is patent and not occluded. While the other options, such as irrigating with heparin, monitoring BP changes, and assessing neurovascular status, are important aspects of dialysis graft care, they are not specifically used for assessing graft patency immediately post-operation.