Ring of the Fisherman cardinal. Ring of the Fisherman The Ring of the Fisherman (Latin: "Annulus Piscatoris"; Italian: "Anello Piscatorio"), also known as the Piscatory Ring, is an official part of the regalia worn by the Pope, who is head of the Catholic Church and successor of Saint Peter who was a fisherman by trade. It used to feature a bas-relief of Peter fishing from a boat, a symbolism derived from the tradition that the apostles were "fishers of men" (Mark 1:17). The Fisherman's Ring is a signet used until 1842 to seal official documents signed by the Pope. A letter written by Pope
Uniquely colorable graph 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 is one that assigns each vertex a different color. Every "k"-tree is uniquely ("k" + 1)-colorable. The uniquely 4-colorable planar graphs are known to be exactly the Apollonian networks, that is, the planar 3-trees . Some properties of a uniquely "k"-colorable graph "G" with "n" vertices and "m" edges: A "minimal imperfect graph" is a graph in which every subgraph is perfect.