## Topology of Graph Configuration Spaces

### Praphat Fernandes

In the Cartesian product of a graph with itself, the subset
consisting of ordered pairs whose coordinates are at least one full
edge apart is called the *N*=2
discretized configuration space of the
graph. This space finds application in the problem of avoiding
collisions of two robots that move on tracks and that can change
direction only at junctions. This paper answers two questions: for
what graphs are the *N*=2
discretized configuration spaces manifolds;
and for what graphs are these spaces pseudomanifolds? The first
answer provides a new proof of a known result; the second answer
appears to be a new result.
(Advisor Peter Haskell)