  We describe the second cohomology of a regular semisimple Hessenberg variety
by generators and relations explicitly in terms of GKM theory. The cohomology
of a regular semisimple Hessenberg variety becomes a module of a symmetric
group $\mathfrak{S}_n$ by the dot action introduced by Tymoczko. As an
application of our explicit description, we give a formula describing the
isomorphism class of the second cohomology as an $\mathfrak{S}_n$-module. Our
formula is not exactly the same as the known formula by Chow or Cho-Hong-Lee
but they are equivalent. We also discuss its higher degree generalization.
