Photonic graph states are underlying resources for one-way optical quantum computation, quantum error correction, fundamental test of quantum mechanics, and quantum communication network. Most of existing works, however, are based on spontaneous parametric down-conversion source that intrinsically suffers from probabilistic generation and double pair components. Here, we create two important classes of graph states, a polarization-encoded four-photon Greenberger-Horne-Zeilinger (GHZ) state and a linear cluster state, by actively demultiplexing a deterministic single photon source from a semiconductor quantum dot embedded in a micropillar. A state fidelity of 0.763±0.004 (0.790±0.009) and a count rate of ∼13 Hz are observed for the four-photon cluster (GHZ) state. The results constitute a new route towards the multiphoton entanglement with deterministic single-photon sources.