  We present a diagrammatic notation to derive the quantum-electrodynamic
coupled cluster (QED-CC) equations needed for the description for polaritonic
ground and excited states. Our presented notation is a generalization of the
existing diagrammatic notation of standard electronic coupled-cluster theory.
Further, we discuss point-group symmetry inside a cavity and its exploitation
within a QED-CC code for efficiency and the targeted treatment of excited
states.
