Chemical graph theory is a subfield of mathematical chemistry which uses the molecular topology to predict the physical properties of a molecule. This Maple worksheet discusses the equivalence between Hückel theory for conjugated hydrocarbons and chemical graph theory for a series of eight benzenoid molecules using Maple's GraphTheory package. Two procedures are written: (1) a procedure which obtains the adjacency matrix, Hückel energies, and normalized eigenvectors from a chemical graph, and (2) a procedure (using the QuantumChemistry package) which obtains the pi molecular orbitals for an actual molecule which correspond to the graph theory MOs from the previous command. This worksheet uses the Maple Quantum Chemistry Toolbox.