  Two signed graphs are called switching isomorphic if one of them is
isomorphic to a switching equivalent of the other. To determine the number of
switching non-isomorphic signed graphs on a specific graph, we will establish a
method based on the action of its automorphism group. As an application and
computational results, we classify all the switching non-isomorphic signed
graphs arising from the complete graph K5 and the generalized Petersen graph
GP(7; 2). Moreover, some results on the automorphism groups of the target
signed graphs are obtained.
