Unimodal general position polynomials

Identify additional graph families whose general position polynomials are unimodal, and determine whether the general position polynomial of every graph corona is unimodal.

Background

The survey explains that general position polynomials are not unimodal for all graphs, although unimodality has been proved for several families, including Kneser graphs K(n,2)K(n,2), combs of paths, and certain complete bipartite graphs. It specifically singles out graph coronas as an unresolved case.

References

Finding other families of unimodal graphs is left as an open question. In particular, it is an open question whether the corona of a graph must always be unimodal.

— The General Position Problem: A Survey  (2501.19385 - V. et al., 31 Jan 2025) in Section 2, subsection “General position polynomials”