  Realizing photonic graph states, crucial in various quantum protocols, is
challenging due to the absence of deterministic entangling gates in linear
optics. To address this, emitter qubits have been leveraged to establish and
transfer the entanglement to photons. We introduce an optimization method for
such protocols based on the local Clifford equivalency of states and the graph
theoretical correlations of the generation cost parameters. Employing this
method, we achieve a 50% reduction in use of the 2-qubit gates for generation
of the arbitrary large repeater graph states and similar significant reductions
in the total gate count for generation of random dense graphs.
