This is the 7421st most frequent Russian word.
графская
"Графская" means "count's" or "pertaining to a count."
Here, 'графская' is used as an adjective meaning 'of the count' or 'belonging to the count', referring to the daughter.
Графская дочка пригласила нас на обед.
The count's daughter invited us for dinner.
In this sentence, 'графская' describes the collection, indicating that it belongs to the count.
В музее представлена графская коллекция картин.
The museum displays the count's collection of paintings.
Here 'графская' is used metaphorically, implying that the decision was made in an authoritative and aristocratic manner.