Final answer:
The central state of an empire can either directly govern its subject states, as seen in the case of the Inca Empire with appointed imperial governors, or rule indirectly, allowing subject states to manage their internal affairs while still being under the central state's influence, illustrated by the concept of suzerainty.
Step-by-step explanation:
The relationship between a central state and subject states within an empire can be categorized into two main forms: direct and indirect rule. Direct rule involves the central government exercising immediate control over the territories of the empire, often administering them through a central bureaucracy and appointing officials to govern on behalf of the central authority. An example is the Inca Empire, where administrative regions were created and governed by imperial governors chosen from the Incan nobility. Indirect rule, on the other hand, allows subject states to maintain their own internal government structures while still being subordinate to the central state, which may exert influence via treaties, alliances, or economic means. In history, relationships might be couched in kinship terms, with the central state seen as the 'father' and the subordinate states as 'children', strengthening the unity and expanding the influence of the empire.