Vipul at 02:32, 28 May 2012

2012-05-28T02:32:40Z

← Older revision		Revision as of 02:32, 28 May 2012
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	{{undirected graph}}		{{undirected graph property}}

	==Definition==		==Definition==
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	# Any two [[adjacent vertices]] of <math>G</math> have precisely <math>\lambda</math> vertices that are adjacent to ''both'' of them.		# Any two [[adjacent vertices]] of <math>G</math> have precisely <math>\lambda</math> vertices that are adjacent to ''both'' of them.
	# Any two ''non''-adjacent vertices of <math>G</math> have precisely <math>\mu</math> vertices that are adjacent to ''both'' of them.		# Any two ''non''-adjacent vertices of <math>G</math> have precisely <math>\mu</math> vertices that are adjacent to ''both'' of them.

			We say that a graph is strongly regular if we can find values of the parameters above for which the graph is strongly regular of that type.

	==Relation with other properties==		==Relation with other properties==

Vipul: Created page with "{{undirected graph}} ==Definition== ===Definition for finite graphs=== Suppose $G$ is a finite undirected graph with $n$ vertices..."

2012-05-28T02:31:49Z

Created page with "{{undirected graph}} ==Definition== ===Definition for finite graphs=== Suppose <matH>G</math> is a finite undirected graph with <math>n</math> vertices..."

New page

{{undirected graph}}

==Definition==

===Definition for finite graphs===

Suppose <matH>G</math> is a [[finite graph|finite]] [[undirected graph]] with <math>n</math> vertices. Suppose <math>d,\lambda,\mu</math> are nonnegative integers. We say that <math>G</math> is a strongly regular graph of type <math>(n,d,\lambda,\mu)</math> (we sometimes write this as <math>\mbox{srg}(n,d,\lambda,\mu)</math>) if it satisfies '''all''' of the following conditions:

# <math>G</matH> is a <math>d</math>-[[regular graph]], i.e., the [[degree of a vertex|degree]] of every [[vertex of a graph|vertex]] of <math>G</math> equals <math>G</math>.
# Any two [[adjacent vertices]] of <math>G</math> have precisely <math>\lambda</math> vertices that are adjacent to ''both'' of them.
# Any two ''non''-adjacent vertices of <math>G</math> have precisely <math>\mu</math> vertices that are adjacent to ''both'' of them.

==Relation with other properties==

===Stronger properties===

{| class="sortable" border="1"
! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
|-
| [[Weaker than::complete graph]] || || || ||
|-
| [[Weaker than::empty graph]] || || || ||
|}

Strongly regular graph - Revision history

Vipul at 02:32, 28 May 2012

Vipul: Created page with "{{undirected graph}} ==Definition== ===Definition for finite graphs=== Suppose G is a finite undirected graph with n vertices..."

Vipul: Created page with "{{undirected graph}} ==Definition== ===Definition for finite graphs=== Suppose $G$ is a finite undirected graph with $n$ vertices..."