Complete graph:K4

This article defines a particular undirected graph, i.e., the definition here determines the graph uniquely up to graph isomorphism.
View a complete list of particular undirected graphs

Definition

This graph is defined as the complete graph on a set of size four.

Arithmetic functions

Size measures

Function	Value	Explanation
size of vertex set	4	As $K_{n},n=4$: $n=4$
size of edge set	6	As $K_{n},n=4$: ${\binom {n}{2}}={\binom {4}{2}}=6$

Numerical invariants associated with vertices

Since the graph is a vertex-transitive graph, any numerical invariant associated to a vertex must be equal on all vertices of the graph. Below are listed some of these invariants:

Function	Value	Explanation
degree of a vertex	3	As $K_{n},n=4$: $n-1=3$
eccentricity of a vertex	1	As $K_{n},n=4$: 1 (true for all $n\geq 2$, independent of $n$)

Other numerical invariants

Function	Value	Explanation
clique number	4	As $K_{n},n=4$: $n=4$
independence number	1	As $K_{n},n=4$: 1 (independent of $n$)
chromatic number	4	As $K_{n},n=4$: $n=4$
radius of a graph	1	Due to vertex-transitivity, the radius equals the eccentricity of any vertex, which has been computed above.
diameter of a graph	1	Due to vertex-transitivity, the radius equals the eccentricity of any vertex, which has been computed above.
odd girth	3	As $K_{n},n=4$: 3 (because $n\geq 3$)
even girth	4	As $K_{n},n=4$: 4 (because $n\geq 4$)
girth of a graph	3	As $K_{n},n=4$: 3 (because $n\geq 3$)