PlanetMath (more info)
 Math for the people, by the people.
Encyclopedia | Requests | Forums | Docs | Wiki | Random | RSS  
Login
create new user
name:
pass:
forget your password?
Main Menu
sections
Encyclopædia
Papers
Books
Expositions

meta
Requests (210)
Orphanage
Unclass'd (1)
Unproven (472)
Corrections (37)
Classification

talkback
Polls
Forums
Feedback
Bug Reports

downloads
Snapshots
PM Book

information
News
Docs
Wiki
ChangeLog
TODO List
Legalese
About
Owner confidence rating: Very low Entry average rating: No information on entry rating
complete graph (Definition)

The complete graph with $ n$ vertices, denoted $ K_n$, contains all possible edges; that is, any two vertices are adjacent.

The complete graph of $ 4$ vertices, or $ K_4$ looks like this:

\includegraphics[scale=1.0]{k4.eps}

The number of edges in $ K_n$ is the $ n-1$th triangular number. Every vertex in $ K_n$ has degree $ n-1$; therefore $ K_n$ has an Euler circuit if and only if $ n$ is odd. A complete graph always has a Hamiltonian path, and the chromatic number of $ K_n$ is always $ n$.



"complete graph" is owned by vampyr.
(view preamble)

View style:

See Also: tournament

Other names:  complete, clique
Log in to rate this entry.
(view current ratings)

Cross-references: chromatic number, Hamiltonian path, odd, Euler circuit, degree, triangular number, adjacent, edges, contains, vertices
There are 27 references to this entry.

This is version 6 of complete graph, born on 2002-02-03, modified 2002-05-27.
Object id is 1757, canonical name is CompleteGraph.
Accessed 9640 times total.

Classification:
AMS MSC: 05C99 (Combinatorics :: Graph theory :: Miscellaneous)
Pending Errata and Addenda
None.
[ View all 1 ]
Discussion
Style: Expand: Order:
forum policy

No messages.

Interact
post | correct | update request | add derivation | add example | add (any)