  In the origins of complexity theory Booth and Lueker showed that the question
of whether two graphs are isomorphic or not can be reduced to the special case
of chordal graphs. To prove that, they defined a transformation from graphs G
to chordal graphs BL(G). The projective resolutions of the associated edge
ideals is manageable and we investigate to what extent their Betti tables also
tell non-isomorphic graphs apart. It turns out that the coefficients describing
the decompositions of Betti tables into pure diagrams in Boij-Soderberg theory
are much more explicit than the Betti tables themselves, and they are expressed
in terms of classical statistics of the graph G.
