Switching a vertex in Σ means negating the signs of all the edges incident to that vertex. Switching a set of vertices means negating all the edges that have one end in that set and one end in the complementary set. Switching a series of vertices, once each, is the same as switching the whole set at once.
Switching of signed graphs (signed switching) is generalized from Seidel (1976), where it was applied to graphs (graph switching), in a way that is equivalent to switching of signed complete graphs.
Switching equivalence means that two graphs are related by switching, and an equivalence class of signed graphs under switching is called a switching class. Sometimes these terms are applied to equivalence of signed graphs under the combination of switching and isomorphism, especially when the graphs are unlabeled; but to distinguish the two concepts the combined equivalence may be called switching isomorphism and an equivalence class under switching isomorphism may be called a switching isomorphism class.
Switching a set of vertices affects the adjacency matrix by negating the rows and columns of the switched vertices. It affects the incidence matrix by negating the rows of the switched vertices.
Read more about this topic: Signed Graph