6. In this problem, tour is the general term referring to both path and ci If a tour starts and ends at the same vertex, then it is a circuit; otherwise, it is a path. In class, we saw that a necessary condition for an undirected graph G-(V, E) to have an Euler tour is that G must have zero or two odd-degree vertices. Now we want to determine what conditions are necessary for a directed graph to have an Euler tour. For a directed graph, we define the in-degree of a vertex , degn (v), to be the nunber of incoming edges into (with arrows pointing towards ) . the out-degree of v, degout(v), to be the number of outgoing edges from v (with arrows pointing away from v), and . the balance of v, balance(v), to be the in-degree of v minus the out-degree of v a) Prove that for any directed graph G- (V, E), balance(v) = 0. b) State (without proof) a necessary condition in terms of balance for a directed graph G(V, E) to have an Euler path. That is, what condition (involving balance) must r condition as an OR statement to encompass the possibility of an Eulerian circuit as well as an Eulerian path that's notia be met to ensure that G has an Euler path Write you circuit c) For each of the following directed graphs, find an Eulerian tour, or say that the graph has no Euler tour