I've constructed a graph in a simular way an interval graph would be constructed from the overlap of intervals. But my intervals are from a modular domain.
Given $\mathit{interval} \equiv \mathit{chordal} \cap \mathit{cocomparability}$ it is obvious the above graph is not an interval graph since it is not chordal. See cycle 2-4-5-6-1-7-2.
My question: is this just a cocomparability graph or does it fall under another classification?