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

Explicit Boij-Soderberg theory of ideals from a graph isomorphism reduction