The bipartite autonomy number of a graph G, marked as ˜α(G), is the minimum value k, where there exist positive integers a and b with a + b = k + 1, that have the characteristic for any two sets A, B ⊆ V (G) with |A| = a and |B| = b, an edge can be found between A and B. McDiarmid and Yolov demonstrated that if δ(G) ≥ α˜(G), G would be Hamiltonian, expanding the renowned theorem initially proposed by Dirac that asserts that if δ(G) ≥ |G|/2 then G is Hamiltonian.