  Our first main result shows that a graph product of right cancellative
monoids is itself right cancellative. If each of the component monoids
satisfies the condition that the intersection of two principal left ideals is
either principal or empty, then so does the graph product. Our second main
result gives a presentation for the inverse hull of such a graph product. We
then specialise to the case of the inverse hulls of graph monoids, obtaining
what we call polygraph monoids. Among other properties, we observe that
polygraph monoids are F*-inverse. This follows from a general characterisation
of those right cancellative monoids with inverse hulls that are F*-inverse.
