Ecclesiastical ring the new pope. The pope's ring is not to be confused with the papal seal, which is what the pope uses to seal documents. The Fisherman's Ring is no longer used to seal anything. Except Pope Benedict XVI, who chose to wear his at all times, the ring had not been seen being publicly worn by a pope since the papacy of Pope Pius XII, who refrained from wearing it once his election ceremonies had been concluded. A collection of rings belonging to the popes of the past is exhibited in a glass case in a room within the papal
Uniquely colorable graph cubic graph is uniquely 3-edge-colorable, it must have exactly three Hamiltonian cycles, formed by the edges with two of its three colors, but some cubic graphs with only three Hamiltonian cycles are not uniquely 3-edge-colorable . Every simple planar cubic graph that is uniquely 3-edge-colorable contains a triangle , but observed that the generalized Petersen graph "G"(9,2) is non-planar, triangle-free, and uniquely 3-edge-colorable. For many years it was the only known such graph, and it had been conjectured to be the only such graph (see and ) but now infinitely many triangle-free non-planar cubic uniquely 3-edge-colorable graphs are known .