Heawood graph - Revision history

Vipul: /* Definition */

2012-05-29T04:23:10Z

Definition

← Older revision		Revision as of 04:23, 29 May 2012
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	The '''Heawood graph''' is an [[undirected graph]] on 14 vertices that can be defined in the following equivalent ways:		The '''Heawood graph''' is an [[undirected graph]] on 14 vertices that can be defined in the following equivalent ways:

	# [[defining ingredient::Levi graph]] of the [[Fano plane]] (which is the [[projective plane]] over [[field:F2]]).		# It is the [[defining ingredient::Levi graph]] of the [[Fano plane]] (which is the [[projective plane]] over [[field:F2]]).
	# It is the unique (up to [[graph isomorphism]]) (3,6)-[[cage]].		# It is the unique (up to [[graph isomorphism]]) (3,6)-[[cage]].

Vipul at 04:22, 29 May 2012

2012-05-29T04:22:50Z

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 ==Definition==
-The '''Heawood graph''' is an [[undirected graph]] on 14 vertices that can be described explicitly as the [[defining ingredient::Levi graph]] of the [[Fano plane]] (which is the [[projective plane]] over [[field:F2]]).
+The '''Heawood graph''' is an [[undirected graph]] on 14 vertices that can be defined in the following equivalent ways:
 ==Arithmetic functions==
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 |-
 | {{arithmetic function value|size of edge set|21}} || As Levi graph of projective plane over <math>\mathbb{F}_q, q = 2</math>: <math>(q + 1)(q^2 + q + 1) = (2 +1)(2^2 + 2 + 1) = 3(7) = 21</math>
 |}

Vipul: Created page with "{{particular undirected graph}} ==Definition== The '''Heawood graph''' is an undirected graph on 14 vertices that can be described explicitly as the [[defining ingredien..."

2012-05-29T04:16:28Z

Created page with "{{particular undirected graph}} ==Definition== The '''Heawood graph''' is an undirected graph on 14 vertices that can be described explicitly as the [[defining ingredien..."

New page

{{particular undirected graph}}

==Definition==

The '''Heawood graph''' is an [[undirected graph]] on 14 vertices that can be described explicitly as the [[defining ingredient::Levi graph]] of the [[Fano plane]] (which is the [[projective plane]] over [[field:F2]]).

==Arithmetic functions==

===Size measures===

{| class="sortable" border="1"
! Function !! Value!! Explanation
|-
| {{arithmetic function value|size of vertex set|14}} || As Levi graph of projective plane over <math>\mathbb{F}_q, q = 2</math>: <math>2(q^2 + q + 1) = 2(2^2 + 2 + 1) = 2(7) = 14</math>
|-
| {{arithmetic function value|size of edge set|21}} || As Levi graph of projective plane over <math>\mathbb{F}_q, q = 2</math>: <math>(q + 1)(q^2 + q + 1) = (2 +1)(2^2 + 2 + 1) = 3(7) = 21</math>
|}