I am reading from the paper here. Let $X$ be a graph and $G$ a finite group which acts on it (as per the definition in the paper, the group action is by default faithful). Now, we say that an edge $e=\pmatrix{d_1 & d_2}$ (where $d_i$ denote darts) is invertible by $G$ if there is some $g\in G$ su...