Please write legibly

(3) Let G be an n-partite simple graph, the partite classes of which are { ui , uj, {u2, v2), . . . , {Un, v.. Assume that the sequence of degrees d(vi), d(u2), d(v2),..., d(un-1), d(vn-1), d(un), d(vn) is some permutation of the integers 0,1,2, 3,...,2n -2. (Note that every vertex except ui is listed. Also, by saying 'permutation', we are not told which degree goes with which vertex.) Deduce what d(ui) and d(vi) are. Justify your answer. (Once you understand what is going on, induction can be an effective way to formulate your proof.) (3) Let G be an n-partite simple graph, the partite classes of which are { ui , uj, {u2, v2), . . . , {Un, v.. Assume that the sequence of degrees d(vi), d(u2), d(v2),..., d(un-1), d(vn-1), d(un), d(vn) is some permutation of the integers 0,1,2, 3,...,2n -2. (Note that every vertex except ui is listed. Also, by saying 'permutation', we are not told which degree goes with which vertex.) Deduce what d(ui) and d(vi) are. Justify your answer. (Once you understand what is going on, induction can be an effective way to formulate your proof.)