HOSIGRA

Resigning: That is to multiply edges incident to a same vertex to a negative sign. One may do this on more than one vertex, that is the same as switching the sign of all edges of an edge-cut of (G, 𝛴 ).

Thus the term "switch" is also used often enough. Toward creating a unified notation we invite everyone to use term "resign" here.

If (G, 𝛴₂ ) is a resigning of (G, 𝛴₁ ) we would say the two signed graphs are equivalent or switch-equivalent.

Observation If G has c connected component, then for any choice of 𝛴 there are 2^n-c signed graphs equivalent to (G, 𝛴 ) (including itself).