Nowhere-zero 3-flow of graphs with small independence number

Tutte's 3-flow conjecture states that every 4-edge-connected graph admits a nowhere-zero 3-flow. In this paper, we characterize all graphs with independence number at most 4 that admit a nowhere-zero 3-flow. The characterization of 3-flow verifies Tutte's 3-flow conjecture for graphs with independence number at most 4 and with order at least 21. In addition, we prove that every odd-5-edge-connected graph with independence number at most 3 admits a nowhere-zero 3-flow. To obtain these results, we introduce a new reduction method to handle odd wheels.