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.

Betrayal

Betrayal is the breaking or violation of a presumptive contract, trust, or confidence that produces moral and psychological conflict within a relationship amongst individuals, between organizations or between individuals and organizations. Often betrayal is the act of supporting a rival group, or it is a complete break from previously decided upon or presumed norms by one party from the others. Someone who betrays others is commonly called a traitor or betrayer. Betrayal is also a commonly used literary element and is often associated with or used as a plot twist.

Definition

Rodger L. Jackson, author of the article, The Sense and Sensibility of Betrayal: Discovering the Meaning of Treachery Through Jane Austen, writes that "there has been surprisingly little written about what we even mean by the term". In psychology, practitioners describe betrayal as the breaking of a social contract; however, critics of this approach claim that the term social contract does not accurately reflect the conditions and motivations for, and effects of, betrayal. Philosophers Judith Shklar and Peter Johnson, authors of The Ambiguities of Betrayal and Frames of Deceit respectively, contend that while no clear definition of betrayal is available, betrayal is more effectively understood through literature.

Betrayal (1932 film)

Betrayal is a 1932 British crime film directed by Reginald Fogwell and starring Stewart Rome, Marjorie Hume and Leslie Perrins. A woman attempts to save her husband from being hanged for a crime he didn't commit. It is based on a play No Crime of Passion by Hubert G. Griffith.

Cast

References

External links

Betrayal (The Following)

"Betrayal" is the twelfth episode of the second season of the psychological thriller television series The Following, which premiered on April 7, 2014, on Fox. It was written by Lizzie Mickery and directed by Marcos Siega.

Summary

Ryan and Claire discuss what happened on the day Ryan was told Claire died. Ryan expresses his disbelief that Claire is actually there and Claire expresses her desire to have Joe dead.

Joe and Emma watch Kingston Tanner, a pastor, in an interview with Carrie where he calls Joe out for being the anti-Christ. Emma asks Joe if he believes in God and Joe says he doesn't. Joe also says he wants to teach Kingston a lesson. Carrie's car gets stuck in traffic behind a big truck. Four of Joe's followers, Angela, Robert, Lucas, and Tilda, attack Carrie's driver and body guard. Tilda hands Carrie a phone with Joe on the line, who informs her she must again broadcast a message of his, or he'll come after her and everyone she loves. Ryan asks Carrie to not broadcast the clip until he watches it, in case it's a message for Joe's followers.