By means of partition technique, a graphical-deleting method for evaluating the char-acteristic polynomial of a graph is proposed in this paper. As colloraries, the Heilbron-ner-Schwenk’s formulas are performed. In comparison with those current methods, thepresent one prevents people from dealing with a lot of subgraphs which originate in delet-ing cycles from the parent graph, thus facilitating working out the characteristic polyno-mial for a polycyclic graph. This seems true even if no topological symmetry is available. As colloraries, the Heilbron-ner-Schwenk’s formulas are performed. In comparison with those current methods, thepresent one of the present-one-partition method, a graphical-deleting method for evaluating the char-acteristic polynomial of a graph is proposed in this paper people from dealing with a lot of subgraphs which originate in delet-ing cycles from the parent graph, thus facilitating working out the characteristic polyno-mial for a polycyclic graph. This seems true even if no topological symmetry is available.