Cage (graph theory)

In the mathematical area of graph theory, a cage is a regular graph that has as few vertices as possible for its girth.

Formally, an (r,g)-graph is defined to be a graph in which each vertex has exactly r neighbors, and in which the shortest cycle has length exactly g. It is known that an (r,g)-graph exists for any combination of r ≥ 2 and g ≥ 3. An (r,g)-cage is an (r,g)-graph with the fewest possible number of vertices, among all (r,g)-graphs.

If a Moore graph exists with degree r and girth g, it must be a cage. Moreover, the bounds on the sizes of Moore graphs generalize to cages: any cage with odd girth g must have at least

vertices, and any cage with even girth g must have at least

vertices. Any (r,g)-graph with exactly this many vertices is by definition a Moore graph and therefore automatically a cage.

There may exist multiple cages for a given combination of r and g. For instance there are three nonisomorphic (3,10)-cages, each with 70 vertices : the Balaban 10-cage, the Harries graph and the Harries–Wong graph. But there is only one (3,11)-cage : the Balaban 11-cage (with 112 vertices).

Cage (enclosure)

A cage is an enclosure made of mesh, bars or wires, used to confine, contain or protect something or someone. A cage can serve many purposes, including keeping an animal in captivity, capturing, and being used for display of an animal at a zoo.

Humans

In history, prisoners were sometimes kept in a cage. They would sometimes be chained up inside into uncomfortable positions to intensify suffering.

History

Cages have been usually been used to capture or trapping a certain life form. For this reason, they've been known as a hunting accessory, often used for poaching animals or simply seizing them.

In captivity

Cages are often used now as a source to confine animals. These provide as a habitat to the animal, and since they've advanced so greatly, they are now specially designed to fit that species of animal. Captive breeds of birds, rodents, reptiles, and even larger animals have also been known to be confined in a cage as a domesticated animal (also known as a pet). Captivity is a common purpose of the cage.

Luke Cage

Luke Cage (born Carl Lucas and also called Power Man) is a fictional superhero appearing in American comic books published by Marvel Comics. Created by Archie Goodwin and John Romita, Sr., he first appeared in Luke Cage, Hero for Hire #1 (June 1972). Imprisoned for a crime he did not commit, he gains superpowers in the form of unbreakable skin and superhuman strength. The character frequently teams up with fellow superhero Iron Fist, and is married to Jessica Jones, with whom he has a daughter. In 2005, writer Brian Michael Bendis added Luke Cage to the lineup of the New Avengers, and he has appeared in various Avengers titles since.

Actor Mike Colter plays the character in Jessica Jones, a live-action television series set in the Marvel Cinematic Universe, and will headline in his own series, which will premiere in 2016.

Publication history

Luke Cage was created by Archie Goodwin and John Romita, Sr. shortly after Blaxploitation films emerged as a popular new genre. He debuted in his own series, Luke Cage, Hero for Hire, which was initially written by Goodwin and pencilled by George Tuska. Cage's adventures were set in a grungier, more crime-dominated New York City than that inhabited by other Marvel superheroes of the time. The series was retitled Luke Cage, Power Man with issue #17.

Silver (Andrew Motion novel)

Silver, subtitled Return to Treasure Island, is a novel by former British Poet Laureate Andrew Motion, published by Jonathan Cape on 15 March 2012. The book follows Jim Hawkins, son of the character of the same name in Robert Louis Stevenson's 1883 novel Treasure Island, as he and Nat, daughter of Long John Silver, also a character in Treasure Island, return to the island visited by their fathers to claim abandoned bar silver.

Silver (Johnny Cash album)

Silver is the 62nd album by American country singer Johnny Cash, released on Columbia Records in 1979. It peaked at #28 on the albums chart. "(Ghost) Riders In The Sky" peaked at #2 on the singles chart; the two other singles, "Bull Rider" and "I'll Say It's True", reached #66 and #42, respectively. Other highlights include "The L & N Don't Stop Here Anymore" and "I'm Gonna Sit on the Porch and Pick on My Guitar". Recordings of "Cocaine Blues" had previously appeared on At Folsom Prison and Now, There Was a Song!, under the title "Transfusion Blues" on the latter. The album also featured production by Brian Ahern, who controversially introduced digital elements into the songs to the disapproval of some listeners. Silver was re-released in 2002 through Legacy Recordings, with remakes of two early Cash songs, "I Still Miss Someone" and "I Got Stripes," as bonus tracks; both are duets with George Jones. This is the last album that Marshall Grant, the original Tennessee Two bass player, played on. He departed from Cash's band the following year.

Silver (film)

Silver - shirubaa is a 1999 Japanese crime film directed by Takashi Miike.

Cast

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