Gain graphs are graphs in which each edge has a gain (a label from a group so that reversing the direction of an edge inverses the gain). In this paper we take a generalized view of gain graphs in which the label of an edge is related to the label of the reverse edge by an involution, i.e., an anti-automorphism of order at most two. Switching classes are equivalence classes of gain graphs under the switching operation. The membership problem is important to the theory of switching classes. The… CONTINUE READING