The graph G, given above, is converted into a weighted graph wG = , as follows: wV = {(A, (1, 23)), (B, (2, 17)), (C, (3, 14)), (D, (4, 6)), (J, (5, 13)), (K, (6, 10)), (P, (5, 1)), (Q, (3, 7)), (R, (2, 5)), (X, (1, 12)), (Y, (4, 13)), ( Z, (6, 19))};

wE = {((A, B), 5), ((A, K), 4), ((A, P), 3), ((B, C), 6), ((B, Q), 3), ((C, D), 2), ((C, R), 3), ((D, J), 4) ((D, X), 2), ((J, K), 2), ((J, Y), 5), ((K, Z), 6), ((P, R),3), ((P, Y), 5), ((Q, X), 4), ((Q, Z), 4), ((R, Y), 1), ((X, Z), 6)}.

Explain what it means to state that a graph algorithm for a graph G = , with m = |V|, and n = |E|, has the complexity as given in each of the following:

a. O(1)

b. O(mn)

c. O(n/m)

d. ?(log(n/m))

e. ?(m+n) ~ ?(n)

f. mn ~ O(m3 ) ~ ? (n2 ).