I've read and heard several times that, reachability graph is a particular type of Transition System, with one initial and UNDEFINED number of final markings.
But if you construct the reachability graph, you have very clear cases of final markings. Does this mean that you can't know which will be your final marking depending on how you fire the transitions? Because, it's obvious that you can enumerate/count the number of final markings.
On
I think you misinterpreted the meaning of "undefined" in this context. To define a reachability graph, you need to specify the states and transitions (a transition system), and you need to specify the initial state. Nothing more, the definition is already complete. The set or number of final states follows from this definition, but it isn't part of the definition, hence "undefined". It would be redundant to include it in the definition.
Compare this with finite automata used as acceptors. There, you must define which states are accepting (=final). Without this information, the definition would be incomplete.
The number of reachable markings in a given reachability graph is possibly undefined. It is undefined in the case of a graph which has an infinite number of reachable markings.