Abstract: Let A_n={a1,a2,…,a_n} and B_n={b1,b1,…,b_n} be two sequences of nonnegative integers with a_i≤b_i for i=1,2,…,n. If A_n and B_n satisfy a1≥a2≥…≥a_n and a_i=a_i+1 implies b_i≥b_i+1 for i=1,2,…,n-1, then A_n and B_n are said to be in good order. If a_i≡b_i(mod 2)for each i and there exists a m-graph G with vertices v1,…,v_n such that a_i≤d_G(v_i)≤b_i and d_G(v_i)≡b_i(mod 2)for each i, then (A_n;B_n) is said to be identical parity m-graphic, G is called a realization of the pair. A constructive method is performed to prove a sufficient condition for (A_n;B_n) to be identical parity m-graphic, where A_n and B_n are in good order.

Key words: degree sequences, constructive method, identical parity m-graphic