Possessive form of pronoun who, the word whose functions as pronoun and determiner in sentences.
1. Whose as pronoun
Whose can function as an interrogative pronoun. An interrogative pronoun (who, whom, whose, what, and which) is a pronoun used to ask direct or indirect questions. Examples:
(Comments are in square brackets.)
Whose is this book?
Whose is the responsibility to park the car?
Can you tell whose this book is? [Indirect question. It’s also known as wh-noun clause. Indirect questions with whose look bit weird. Determiners are a more natural way of asking such questions]
I wonder whose responsibility to park the car is. [Indirect question]
Some mistakenly treat whose introducing a noun clause as subordinating conjunction. That’s because, in common parlance, the term subordinating conjunction is associated with any word that joins a dependent clause to an independent clause. But in noun clauses, none of wh-elements (how, when, where, why, who, whom, whose, what, which) is a subordinating conjunction. They are either interrogative adverb, interrogative pronoun, or interrogative determiner. Whose, for example, functions as interrogative pronoun and determiner.
2. Whose as determiner
Whose can be an interrogative or a relative determiner.
2.1 Interrogative determiner
Whose can function as an interrogative determiner. (Some grammar books term it as interrogative adjective.) An interrogative determiner (what, which, and whose), while asking a direct or indirect question, modifies a noun and is placed immediately before it. Examples:
Whose book is this?
Whose responsibility is it to park the car?
Can you tell whose book this is? [The sentence ends with a question mark because the main clause is an interrogative sentence]
I wonder whose responsibility it is to park the car.
2.2 Relative determiner
Whose can also be used as relative determiner, where it connects a relative clause to the preceding noun phrase. Examples:
The author whose book was launched at the literary fest received high praise.
The house, whose walls developed cracks in the recent earthquake, needs to be demolished urgently.
Note that unlike who and whom, whose does not function as relative pronoun. It functions as relative determiner in introducing relative clauses.
Some mistakenly treat whose introducing relative clauses as subordinating conjunction. This error though is less common than the one in noun clause. But whose, in this role, is a determiner – relative determiner – and not conjunction.
If you noticed, whose introduces two dependent clauses – relative and noun clause. Since it doesn’t introduce adverb clause, it’s not a subordinating conjunction.