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 A uniquely total colorable graph is a "k"-total-chromatic graph that has only one possible (proper) "k"-total-coloring up to permutation of the colors. Empty graphs, paths, and cycles of length divisible by 3 are uniquely total colorable graphs. Some properties of a uniquely "k"-total-colorable graph "G" with "n" vertices: Here χ″("G") is the total chromatic number; Δ("G"), maximum degree; and δ("G"), minimum degree. Uniquely colorable graph In graph theory, a uniquely colorable graph is a k-chromatic graph that has only one possible (proper) "k"-coloring up to permutation of the colors. A complete graph is uniquely colorable, because the only proper coloring