Vipul at 17:48, 28 May 2012

2012-05-28T17:48:34Z

← Older revision		Revision as of 17:48, 28 May 2012
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	# <math>G</matH> is a [[graph of finite diameter]] and its [[defining ingredient::radius of a graph\|radius]] equals its [[defining ingredient::diameter of a graph\|diameter]].		# <math>G</matH> is a [[graph of finite diameter]] and its [[defining ingredient::radius of a graph\|radius]] equals its [[defining ingredient::diameter of a graph\|diameter]].
	# The [[eccentricity of a vertex\|eccentricity]] of every vertex of <math>G</math> is equal to a fixed finite number.		# The [[eccentricity of a vertex\|eccentricity]] of every vertex of <math>G</math> is equal to a fixed finite number.

			==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::vertex-transitive finite connected graph]] \|\| \|\| \|\| \|\|
			\|-
			\| [[Weaker than::vertex-transitive graph of finite diameter]] \|\| \|\| \|\| \|\|
			\|}

			===Weaker properties===

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

Vipul: Created page with "{{undirected graph property}} ==Definition== Suppose $G$ is a connected undirected graph. We say that $G$ is a '''graph of cons..."

2012-05-28T17:47:39Z

Created page with "{{undirected graph property}} ==Definition== Suppose <math>G</math> is a connected undirected graph. We say that <math>G</math> is a '''graph of cons..."

New page

{{undirected graph property}}

==Definition==

Suppose <math>G</math> is a [[connected graph|connected]] [[undirected graph]]. We say that <math>G</math> is a '''graph of constant finite eccentricity''' if it satisfies the following equivalent conditions:

# <math>G</matH> is a [[graph of finite diameter]] and its [[defining ingredient::radius of a graph|radius]] equals its [[defining ingredient::diameter of a graph|diameter]].
# The [[eccentricity of a vertex|eccentricity]] of every vertex of <math>G</math> is equal to a fixed finite number.

Graph of constant finite eccentricity - Revision history

Vipul at 17:48, 28 May 2012

Vipul: Created page with "{{undirected graph property}} ==Definition== Suppose G is a connected undirected graph. We say that G is a '''graph of cons..."

Vipul: Created page with "{{undirected graph property}} ==Definition== Suppose $G$ is a connected undirected graph. We say that $G$ is a '''graph of cons..."