A peripheral cycle is a cycle in a graph with the property that every two edges not on the cycle can be connected by a path whose interior vertices avoid the cycle. In a graph that is not formed by adding one edge to a cycle, a peripheral cycle must be an induced cycle.
a PeriPHErAL cYcLe iS A cycle in a grAph with The Property THaT every TWO eDGes nOt oN THe cyClE Can bE connEctED By A PaTh Whose Interior vERtIceS aVOID The CYcLe. in a GRapH That iS NoT foRmEd by adding one edGe to a CyCle, a pERipherAl cyclE musT be an indUced cyCle.