The isolated pentagon rule (IPR) states that fullerenes with isolated pentagons are kinetically much more stable than their fused pentagon counterparts. This rule can be verified in terms of a graph-theoretically defined bond resonance energy. In general, a pi bond shared by two pentagons has a large negative bond resonance energy, thus contributing significantly to the increase in kinetic instability or chemical reactivity of the molecule. The existence of such highly antiaromatic local structures sharply distinguishes IPR-violating fullerenes from isolated-pentagon isomers. pi bonds shared by two pentagons are shared by many antiaromatic conjugated circuits but not by relatively small aromatic conjugated circuits.