How to categorize an undirected triangular graph with top, bottom, and intertwining paths
Your algorithm relies on some properties of the input graph for its correctness. You should isolate these properties, and then you will know how to name your program.

The most likely answer is that your algorithms works on DAGs oriented source-to-sink, as you and David mention. However, there are many possible variants:


Your algorithm might rely on the DAG having a single source.
Your algorithm might rely on the outdegree being at most 2 or perhaps exactly 0 or 2.
Your algorithm might work on every (possibly connected) graph, implicitly considering say the BFS tree (or forest) of the graph, from a given starting node.


Only you can tell which of these is correct for your algorithm.