K n . Simple complete graph of order n .
Summary
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- 1
- 1 Adjacency matrix.
- 2 Graphic representation.
- 3 See also.
- 4
Characteristics.
The family of graphs K n is the simplest of the nonoriented graphs of equivalent order since they do not have neither multiarists nor ties but they achieve, since they are complete, the existence of an edge between any pair of different nodes.
This produces minimal paths between any pair of vertices.
Adjacency matrix.
The adjacency matrix in the K n family is easy to recognize since all its elements have a value of 1, except those of the main diagonal, which are 0.
Then, the powers of said matrix will always be non-zero, identifying the fact that there are always paths of any order between the nodes.
Graphic representation.
K 2 are two vertices joined by an edge.
The K n are usually represented as the same regular polygons of equivalent order: the vertices of both are equalized and then the edges are drawn between all the pairs of vertices.
This form of representation allows us to obtain figures known as the equilateral triangle ; the 5-pointed star within the pentagon (seen in ancient texts associated with magic and alchemy ); the hexagon with 2 equilateral triangles inscribed opposite each other and others that present great harmony and visual complexity.
