I want to delete a vertex and all vertexes that point to it where the edges between them are from a set of labels - not necessarily all the incoming vertexes.
In a relational database you can configure automatic deletion of related entities using cascading deletes on foreign keys.
Is there a similar configuration expressible in Titan DB or with Gremlin?
There is no such feature in Titan at this time. You would have to manage such logic manually as part of your delete of the vertex: