Homomorphisms of signed graphs: An update

A signed graph is a together with an assignment of signs to the edges. closed walk in said be positive (negative) if it has even (odd) number negative edges, counting repetition. Recognizing walks as one key structural properties graph, we define homomorphism (G,?) (H,?) mapping vertices and edges G (respectively) H which preserves incidence, adjacency walks. In this work first give characterization sets that correspond set some on G. We also easy algorithm for corresponding decision problem. After verifying equivalence between definition earlier ones, discuss relation homomorphisms graphs those 2-edge-colored graphs. Next provide basic no-homomorphism lemmas. These lemmas lead general method defining chromatic discussed at length. Finally, list few problems are driving force behind study