Determining connectivity for a fully dynamic graph with vertex/subgraph insertion and deletion I am looking for a solution to the following problem and wonder if anyone could point me to some existing research on this topic. I am coming from a real world application of graph so bear with me if my terminology is not exactly right. 

I have a database system where user can add/remove/move objects by creating/deleting and altering relationships. As such, I can see the objects as been vertices in a graph and the relationships been edges and edges can be weighted depending on the type of relationships (either composition, association, or aggregation). 

From the user's point of view, adding a new element can be a single click and underneath the hood, the program creates a graph of objects linked by relationships. This graph, is then added to the main graph that defines the entire database. Removing an element, would be the reverse where links/edges are disconnected and the graph becomes two disjoint graphs where 1 is the database, and the other consists of vertices formed by the element and its sub elements.

I need a really quick way to determine when I have a disjoint graphs and when 2 disjoint graphs becomes 1 again. I had a brief look at Holm, de Lichtenberg, and Thorup (2001; pdf). It seems like the way to go, but the author did mention they are only considering a graph with fixed number of vertices. Just wondering do algorithms usually extend themselves to adding/removal of vertices by just performing the adding of edges incrementally? Or has there been works that tailors specifically for such scenario?
This isn't a trivial question at all. One of the problems you'll have finding algorithms for this is the disconnectedness (pun intended) of the work on dynamic graphs. Thorup et al.'s work (the one you mention) is probably the best start for the kind of thing you're looking for.

You could also try Bhadra &amp; Ferreira, they're probably getting a bit off-topic for what you want, but they do have references to other material that could be useful.