Correct!   The right gastric artery arises from the proper hepatic artery and courses around the lesser curvature of the stomach. As the lesser curvature remains (the new stomach on the diagram), the right gastric artery must remain intact to supply that remaining stomach tissue with blood.

Incorrect. The left gastric artery arises from the celiac trunk and courses around the lesser curvature of the stomach. As the lesser curvature remains (the new stomach on the diagram), the left gastric artery must remain intact to supply that remaining stomach tissue with blood.

Incorrect. The splenic artery supplies the spleen and stomach via additional branches. Thus, while some of those secondary branches to the stomach may need ligating, the main feeder vessel to the spleen would not be ligated.

Correct!  The short gastric arteries branch from the splenic artery and supply the fundus of the stomach. As this region was removed, any short gastric arteries must be ligated.   

Correct. The left gastro-omental artery branches from the splenic artery and course around the greater curvature of the stomach. As this region was removed, the left gastro-omental artery must be must be ligated. 

Correct! The right gastro-omental artery branches from the gastroduodenal artery and course around the greater curvature of the stomach. As this region was removed, the right gastro-omental artery must be must be ligated. 

Incorrect. While the artery has 'gastric' in the name, the inferior epigastric artery supplies the rectus abdominis muscle and anterior abdominal wall.

Incorrect. The gastroduodenal artery supplies multiple organs including the stomach via additional branches. Thus, while some of those secondary branches may need ligation the main feeder vessel of the gastroduodenal would not be ligated.