Ok so this is how I solve a pedigree:
This clearly shows that the disease is autosomal dominant. But there is one problem.
An autosomal dominant pedigree has the following features:
1. Appears in both sexes with equal frequency.
2. Both sexes transmit the trait to the offspring.
3. Doesn’t skip generations.
4. When one parent (heterozygous) is affected, and the other parent is unaffected, there is a 50% chance of the offspring getting affected. (You can refer to the cross I’ve drawn below your picture)
The pedigree in the question satisfies all 3 points except the last one. If there are 6 offsprings, at least 2 of them should be affected (if not 3), but there is only one, and that too a male.
Since only the male is affected in all generations, you’re right in thinking it’s Y linked. In my opinion, it can be Y linked dominant, since that’s very rare. And your question specifies that the trait is rare. It could DEFINITELY be autosomal dominant, had there been more affected offsprings in the third generation.