Complete Graph
In the
mathematical
field of
graph theory
a
complete graph
is a
simple graph
where an
edge
connects every pair of
vertices
. The
complete graph on
n
vertices
has
n
vertices and
n(n-1)/2
edges, and is denoted by
K_n
. It is a
regular graph
of
degree
n-1
. All complete graphs are their own
cliques
. They are maximally
connected
as the only
vertex cut
which disconnects the graph is the complete set of vertices. A
planar graph
cannot contain
K_5
(or the
complete bipartite graph
K_{3,3}
) as a
minor
. Complete graphs on
n
vertices, for
n
between 1 and 8, are shown below:
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