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 The deletion of any vertex from a minimal imperfect graph leaves a uniquely colorable subgraph. A uniquely edge-colorable graph is a "k"-edge-chromatic graph that has only one possible (proper) "k"-edge-coloring up to permutation of the colors. The only uniquely 2-edge-colorable graphs are the paths and the cycles. For any "k", the stars "K" are the only uniquely "k"-edge-colorable graphs. Moreover, conjectured and proved that, when "k" ≥ 4, they are also the only members in this family. However, there exist uniquely 3-edge-colorable graphs that do not fit into this classification, such as the graph of the triangular pyramid. If a