This study analyzes the solution to the max-cut problem of different vertices according to quantum adiabatic approximation. In this algorithm, the vertices of an undirected graph are equivalent to qubits, the edge between vertices to the coupling between two qubits, and the weight value of an edge to the coupling strength. The algorithm is written in the Python programming language, and the solution to the max-cut problem of a completely undirected graph with 6–13 vertices is simulated. Experimental results demonstrate that when the completely undirected graph has 8, 12, and 13 vertices and coupling strength is 1.0, the expected value of Hamiltonian in the max-cut problem does not converge. Then the coupling strength between qubits is adjusted to observe the changes in the expected value. Experiments reveal that for a completely undirected graph with 12 vertices, the expected value converges when coupling strength is 0.95. For completely undirected graphs with 8 and 13 vertices, it converges with time when coupling strength is 0.75. Accordingly, it is inferred that the coupling strength between qubits can be normalized to about 0.75 when the quantum adiabatic algorithm is used to solve the max-cut problem for a completely undirected graph with more than 13 vertices, so that the expected value can eventually converge.