Complete graph:K4 - Revision history

Vipul: /* Definition */

2012-05-29T21:21:09Z

Definition

← Older revision		Revision as of 21:21, 29 May 2012
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	==Definition==		==Definition==

	This graph, denoted <math>K_4</math> is defined as the [[complete graph]] on a set of size four. It is also sometimes termed the '''tetrahedron graph''' or ''tetrahedral graph'''.		This graph, denoted <math>K_4</math> is defined as the [[complete graph]] on a set of size four. It is also sometimes termed the '''tetrahedron graph''' or '''tetrahedral graph'''.

	==Explicit descriptions==		==Explicit descriptions==

2012-05-29T19:51:32Z

← Older revision		Revision as of 19:51, 29 May 2012
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	==Definition==		==Definition==

	This graph, denoted <math>K_4</math> is defined as the [[complete graph]] on a set of size four. It is also sometimes termed the ''tetrahedron graph''' or ''tetrahedral graph'''.		This graph, denoted <math>K_4</math> is defined as the [[complete graph]] on a set of size four. It is also sometimes termed the '''tetrahedron graph''' or ''tetrahedral graph'''.

	==Explicit descriptions==		==Explicit descriptions==

2012-05-29T19:51:22Z

← Older revision		Revision as of 19:51, 29 May 2012
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	This graph, denoted <math>K_4</math> is defined as the [[complete graph]] on a set of size four. It is also sometimes termed the ''tetrahedron graph''' or ''tetrahedral graph'''.		This graph, denoted <math>K_4</math> is defined as the [[complete graph]] on a set of size four. It is also sometimes termed the ''tetrahedron graph''' or ''tetrahedral graph'''.

			==Explicit descriptions==

			===Descriptions of vertex set and edge set===

			Vertex set: <math>\{ 1,2,3,4 \}</math>

			Edge set: <math>\{ \{ 1,2 \}, \{ 1,3 \}, \{ 1,4 \}, \{ 2,3 \}, \{ 2, 4 \}, \{ 3, 4 \} \} </math>

			===Adjacency matrix===

			The adjacency matrix is:

			<math>\begin{pmatrix} 0 & 1 & 1 & 1\\ 1 & 0 & 1 & 1 \\ 1 & 1 & 0 & 1 \\ 1 & 1 & 1 & 0\\\end{pmatrix}</math>

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

	==Arithmetic functions==		==Arithmetic functions==

2012-05-29T19:48:54Z

← Older revision		Revision as of 19:48, 29 May 2012
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	==Definition==		==Definition==

	This graph is defined as the [[complete graph]] on a set of size four.		This graph, denoted <math>K_4</math> is defined as the [[complete graph]] on a set of size four. It is also sometimes termed the ''tetrahedron graph''' or ''tetrahedral graph'''.

	==Arithmetic functions==		==Arithmetic functions==

2012-05-29T19:45:11Z

Other numerical invariants

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 |-
 | {{arithmetic function value|girth of a graph|3}} || As <math>K_n, n = 4</math>: 3 (because <math>n \ge 3</math>)
 |}

2012-05-29T03:56:37Z

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 |-
 | {{arithmetic function value|size of edge set|6}} || As <math>K_n, n = 4</math>: <math>\binom{n}{2} = \binom{4}{2} = 6</math>
 |}

2012-05-29T03:53:44Z

← Older revision		Revision as of 03:53, 29 May 2012
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	This graph is defined as the [[complete graph]] on a set of size four.		This graph is defined as the [[complete graph]] on a set of size four.

			==Arithmetic functions==

			===Size measures===

			{\| class="sortable" border="1"
			! Function!! Value !! Explanation
			\|-
			\| {{arithmetic function value\|size of vertex set\|4}} \|\| As <math>K_n, n = 4</math>: <math>n = 4</math>
			\|-
			\| {{arithmetic function value\|size of edge set\|6}} \|\| As <math>K_n, n = 4</math>: <math>\binom{n}{2} = \binom{4}{2} = 6</math>
			\|}

2012-05-29T03:36:39Z

← Older revision		Revision as of 03:36, 29 May 2012
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	{{particular graph}}		{{particular undirected graph}}

	==Definition==		==Definition==

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

2012-05-29T03:36:17Z

Created page with "{{particular graph}} ==Definition== This graph is defined as the complete graph on a set of size four."

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{{particular graph}}

==Definition==

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