Let S' be the set of connected graphs such that there exists a function w : E(G) - {+1, -1 } satisfying E w([u, v]) = 0 for all DE V(G). "EV(G):[HD) CE(G) (a) Suppose that G E S. Show that G has an Eulerian circuit. (b) Suppose that G is a bipartite connected graph that has an Eulerian circuit. Show that GE S. (c) Give an example of a connected graph G which has an Eulerian circuit and such that G E S