Realization of graphs by fold Gauss maps (Q1688220)

In their previous paper [Bull. Braz. Math. Soc. (N.S.) 42, No. 1, 87--103 (2011; Zbl 1222.57032)], the authors developed an approach in the study of surfaces generically immersed in \(\mathbb R^3\) based on properties of weighted graphs. The main goal of the paper under review is to prove that a graph with total weight equal to zero is a graph corresponding to a fold (i.e., without cusps) Gauss map of a closed orientable surface if and only if it is a 2-negative graph.