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Yes, the Afghan Hound is classified as a sighthound, or, more broadly, a Hound.
The Afghan Hound is in the Sighthounds Group (Group 10).
No, the Afghan Hound is not available in all version of Nintendogs and Nintendogs and Cats.
The Afghan Hound has the longest coat among the sighthounds. If left untrimmed, an Afghan Hound's coat can almost reach the ground.
Read more about the Afghan Hound in the related links.
No, "Persian Greyhound" is another name for the Saluki, which is a different breed from the Afghan Hound (known as "Afghan" for short).