Connectedness of graphs arising from the dual Steenrod algebra

Abstract

We establish connectedness criteria for graphs associated to monomials in certain quotients of the mod 2 dual Steenrod algebra \(\mathscr {A}^*\). We also investigate questions about trees and Hamilton cycles in the context of these graphs. Finally, we improve upon a known connection between the graph theoretic interpretation of \(\mathscr {A}^*\) and its structure as a Hopf algebra.