Based upon our previous works, a systematic mathematical demonstration of polycyclic aromatic hydrocarbons (PAH) graphs has been carried out in this laboratory. The uniqueness of characteristic number (linear topology notation of PAH), the even number theorem for the discriminating of complete aromaticity for PAH in structure prediction and enumeration, the transformation theorem from the characteristic number to form the adjacency matrix uniquely, the diserote mathematics strategy for the programming of the automatic MO calculation to a whole class of compounds as well as the other aspects have been demonstrated in this paper. In terms of these research, the wholesale molecular orbital calculation (WMO) and the linear notation containing all the topologic information of PAH molecule have been put forward for the first time, so the first example for the structure prediction and enumeration of PAH having truly chemical significance as well as automatic, systematic MO calculation of whole compound class h Based upon our previous works, a systematic mathematical demonstration of polycyclic aromatic hydrocarbons (PAH) graphs has been carried out in this laboratory. The uniqueness of characteristic number (linear topology not PAA), the even number theorem for the discriminating of complete aromaticity for PAH in structure prediction and enumeration, the transformation theorem from the characteristic number to form the adjacency matrix uniquely, the diserote mathematics strategy for the programming of the automatic MO calculation to a whole class of compounds as well as the other aspects have been demonstrated in this paper. In terms of these research, the wholesale molecular orbital calculation (WMO) and the linear notation containing all the topologic information of PAH molecule have been put forward for the first time, so the first example for the structure prediction and enumeration of PAH having truly chemical significance as well as automatic, systematic MO calculation of whol e compound class h