Pārāśara's Ch. 3 is the canonical chapter on graha-kārakatva — what each graha rules and signifies. This is the second leg of the two-pointer interpretive system: the bhāva tells you the life-domain, the kāraka tells you the graha most-specifically-tied to that domain. When the bhāva-lord is weak but the kāraka is strong, the domain-signification still flows through the kāraka's pathway.
Each graha has multi-layered kārakatva: a natural-kāraka (e.g., Jupiter for children), a body-kārakatva (Sūrya for the head/heart, Candra for blood/lungs), a domain-kārakatva (Sūrya for government, Maṅgala for the military, Bṛhaspati for academia and law). BPHS Ch. 14 enumerates these explicitly.