The effects of different types of boundaries on graphite fragments are considered as they influence the pi-electrons. From a simple resonance theoretic argument there are proposed simple structural conditions governing the occurrence of "unpaired" pi-electron density near the edges. Predictions based on these rules are made for a variety of edge structures. Further, the novel resonance theoretic argument and predictions are strengthened through more elaborate considerations of both The valence bond and molecular orbital theoretic nature, especially for translationally symmetric polymer strips with Various types of edges.