Complete graph:K5

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, denoted $K_{5}$, is defined as the complete graph on a vertex set of size 5.

Explicit descriptions

Descriptions of vertex set and edge set

Vertex set: $\{1,2,3,4,5\}$

Edge set: $\{\{1,2\},\{1,3\},\{1,4\},\{1,5\},\{2,3\},\{2,4\},\{2,5\},\{3,4\},\{3,5\},\{4,5\}\}$

Adjacency matrix

The adjacency matrix is:

${\begin{pmatrix}0&1&1&1&1\\1&0&1&1&1\\1&1&0&1&1\\1&1&1&0&1\\1&1&1&1&0\\\end{pmatrix}}$

The matrix is uniquely defined (note that it centralizes all permutations).