  This article generalizes the operad of moduli spaces of curves to SUSY
curves. SUSY curves are algebraic curves with additional supersymmetric or
supergeometric structure. Here, we focus on the description of the relevant
category of graphs and its combinatorics as well as the construction of dual
graphs of SUSY curves and the SUSY operad taking values in a category of moduli
spaces of SUSY curves with Neveu-Schwarz and Ramond punctures.
