Defining Path
You are right to be confused if your professors did not clarify (see warning at end). The term "path" can mean a few things:
"Concrete" Path:
Recall, a graph is a collection of vertices and edges. A path on the graph is then:
$$v_1\xrightarrow{e_1} v_2\xrightarrow{e_2} \cdots \xrightarrow{e_{n-1}} v_n$$
Where $v_i$ are vertices on the graph and the arrows denote the direction traversed over the undirected edges $e_j$. Observe, this definition explicitly defines some "chain" of vertices connected by specific edges.
"Abstract" Path: Say there is some task that involves a serious of repeated actions but does not depend on specific objects. We can define this as a chain of composed functions:
$$f_n\circ\cdots \circ f_1$$
The idea, is that this definition is little more abstract. Though, there are many other ways one could define "path."
"Solution Path"
A Subtlety
So, in this case, is the solution path A -> B -> C, i.e. the order in which the nodes are visited? Or is the solution path A -> B -> A -> C? Basically saying that we go from A to B, but to go from B to C, we must go through A again.
BFS does not "go through A again." Considering you are using a queue based implementation, once A has been visited there will be no need to "visit" it again. That is, we have added all nodes we need to the queue and marked A as being seen. This leads into:
How to report the solution path of a search algorithm on a graph?
Since, these algorithms do not revisit nodes, what is most likely being asked of you is for you to report the order of the visits - this is what my professors wanted in my AI & Algorithms courses.
A Warning: I can only answer what my professors wanted. Please clarify this with your instructors.
