Lewis Carrol Doublets solver by Graham Toal.  Breadth-first search
over word list.  Guarantees to find shortest path.

Written in Pascal.  Use p2c or take C source if you can't be bothered.

See a similar algorithm, probably better written, certainly better
described, in ../sgb (Stanford Graph Base) where it is one of the
demonstration examples for a general purpose Graph manipulation package
by Donald Knuth.  (If you don't know who Don Knuth is, you shouldn't
be in the programming business.)