Rooted digraphs are used to represent the features of a protonated water (PW) cluster, and we obtain all possible topology-distinct patterns corresponding to PW clusters containing up to seven water molecules. From close investigation of the structural patterns obtained, several restrictions that should be satisfied in the stable structures of PW clusters are found. The generated hydrogen bond (HB) matrices of the restrictive rooted digraph are used as the theoretical framework to obtain all of the local minima on the potential energy surfaces of those PW clusters by the use of ab initio MO and DFT methods. For PW pentamers, hexamers, and heptamers, some new local minimum structures were found that were not previously obtained. We classify all of the O-H bonds in PW clusters up to heptamer into nine types according to the difference in the hydrogen bonding pattern; each type is accompanied by a specific range of stretching frequency. The ranges of stretching frequencies of different types of O-H in PW clusters are systematically classified.