please answer quetions below

Under what conditions does a graph have an Euler circuit? '12:} A. A graph has an Euler circuit if it is connected and every vertex has even degree. if} B. A graph has an Euler circuit if it is connected and has an even number of edges. {2:} C. A graph has an Euler circuit if it is connected and has an even number of vertices. '12-} D. A graph has an Euler circuit if every vertex has even degree. if} E. none of the above After the eulerization of a graph, how many odd vertices are there? . . . O A. the same as the number of odd vertices before the eulerization O B. 2 O C. not possible to determine without knowing the specific graph O D. the same as the number of even vertices of the graph OE. 0Determine which of the following graphs shows an optimal eulerization. Choose the correct graph below. L h m. r e In t D t h p m g e In t r (m n .m t a .2 r m u e m .m t p O n a d .m F For the graph, complete parts (a) through (c). . . . (a) Identify three different Hamilton circuits from the following choices. Select all that apply. A. E, F, A, B, C, D, G, E B. E, C, D, B, G, F, A, E C. E, A, F, B, G, D, C, E D. E, D, F, A, C, B, G, E E. E, C, D, G, B, F, A, E F. E, C, F, D, G, B, A, E (b) Find a Hamilton path that starts at A and ends at B. (Use a comma to separate vertices as needed.) (c) Find a Hamilton path that starts at A and ends at F. (Use a comma to separate vertices as needed.)For the graph shown on the right, find the following. 6.2.5 (a) Find the Hamilton path that starts at A and ends at F. (b) Find the Hamilton circuit that starts at A and ends with the edge FA. (c) Find the Hamilton path that starts at A and ends at B. (d) Find a Hamilton path that starts at C and ends at G. . . . (a) What is the Hamilton path that begins at A and ends at F? (Use a comma to separate vertices as needed.) (b) What is the Hamilton circuit that starts at A and ends with the edge FA? (Use a comma to separate vertices as needed.) (c) What is the Hamilton path that begins at A and ends at B? (Use a comma to separate vertices as needed.) (d) What is a Hamilton path that begins at C and ends at G? (Use a comma to separate vertices as needed.)Find an optimal tour for the TSP (traveling salesman problem) to the right, and give its cost. Find an optimal tour using the brute-force algorithm. (Use a comma to separate vertices as needed.) What is the cost of the optimal tour'? (Type a whole number.)