Photonic graph states constitute important resources in quantum information processing. They are used in measurement-based and fusion-based quantum computing and in all-photonic repeaters for quantum networks. However, generating such highly entangled states is challenging due to the fact that photons do not interact with each other. I will introduce approaches for the generation of certain multi-photon entangled states from quantum emitters, which is--in principle--deterministic. I will also present a general protocol for generating arbitrary graph states using the least number of matter qubits as emitters. Our algorithm provides not only the number of emitters required but also, in polynomial time, the quantum circuit for the graph state generation (which includes the non-unitary process of photon emission). We find that the quantum circuit depth for general graphs also scale polynomially with system size.