Complete graph:K5: Difference between revisions
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==Definition== | ==Definition== | ||
This graph, denoted <math>K_5</math>, is defined as the [[complete graph]] on a set of size 5. | This graph, denoted <math>K_5</math>, is defined as the [[complete graph]] on a vertex set of size 5. | ||
==Explicit descriptions== | |||
===Descriptions of vertex set and edge set=== | |||
Vertex set: <math>\{ 1,2,3,4,5 \}</math> | |||
Edge set: <math>\{ \{ 1,2 \}, \{ 1,3 \}, \{ 1,4 \}, \{ 1, 5 \}, \{ 2,3 \}, \{ 2,4 \}, \{ 2,5 \}, \{ 3,4 \}, \{ 3, 5 \}, \{ 4, 5 \} \}</math> | |||
===Adjacency matrix=== | |||
The adjacency matrix is: | |||
<math>\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}</math> | |||
The matrix is uniquely defined (note that it centralizes all permutations). | |||
Latest revision as of 21:23, 29 May 2012
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 , is defined as the complete graph on a vertex set of size 5.
Explicit descriptions
Descriptions of vertex set and edge set
Vertex set:
Edge set:
Adjacency matrix
The adjacency matrix is:
The matrix is uniquely defined (note that it centralizes all permutations).