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

Graph products of right cancellative monoids