Vipul at 17:32, 28 May 2012

2012-05-28T17:32:06Z

← Older revision		Revision as of 17:32, 28 May 2012
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	==Definition==		==Definition==

	Suppose <math>G</math> is a [[connected graph\|connected]] [[undirected graph]] that has a finite [[defining ingredient::radius of a graph\|radius]]. (Note that any finite connected undirected graph must have finite radius, but infinite graphs may sometimes have finite radius). A vertex <math>v</math> of <math>G</math> is termed a '''central vertex''' if the [[defining ingredient::eccentricity of a vertex\|eccentricity]] of <math>v</math> (i.e., the maximum of distances between <math>v</math> and vertices of <math>G</math>) equals the radius of <math>G</math>. Note that the radius is defined as the minimum of the eccentricities of all vertices.		Suppose <math>G</math> is a [[graph of finite diameter]], i.e., it is a [[connected graph\|connected]] [[undirected graph]] that has a finite [[defining ingredient::radius of a graph\|radius]]. (Note that any finite connected undirected graph must have finite radius, but infinite graphs may sometimes have finite radius). A vertex <math>v</math> of <math>G</math> is termed a '''central vertex''' if the [[defining ingredient::eccentricity of a vertex\|eccentricity]] of <math>v</math> (i.e., the maximum of distances between <math>v</math> and vertices of <math>G</math>) equals the radius of <math>G</math>. Note that the radius is defined as the minimum of the eccentricities of all vertices.

	==Facts==		==Facts==

Vipul: Created page with "{{undirected graph vertex property}} ==Definition== Suppose $G$ is a connected undirected graph that has a finite [[defining ingredient::r..."

2012-05-28T17:22:21Z

Created page with "{{undirected graph vertex property}} ==Definition== Suppose <math>G</math> is a connected undirected graph that has a finite [[defining ingredient::r..."

New page

{{undirected graph vertex property}}

==Definition==

Suppose <math>G</math> is a [[connected graph|connected]] [[undirected graph]] that has a finite [[defining ingredient::radius of a graph|radius]]. (Note that any finite connected undirected graph must have finite radius, but infinite graphs may sometimes have finite radius). A vertex <math>v</math> of <math>G</math> is termed a '''central vertex''' if the [[defining ingredient::eccentricity of a vertex|eccentricity]] of <math>v</math> (i.e., the maximum of distances between <math>v</math> and vertices of <math>G</math>) equals the radius of <math>G</math>. Note that the radius is defined as the minimum of the eccentricities of all vertices.

==Facts==

* [[Tree has either one central vertex or two adjacent central vertices]]
* [[Connected graph may have precisely two non-adjacent central vertices]]

==Related properties==

* [[Peripheral vertex]] is in some sense the opposite: it is a vertex whose eccentriciti equals the diameter, which is the maximum of all eccentricities.

Central vertex - Revision history

Vipul at 17:32, 28 May 2012

Vipul: Created page with "{{undirected graph vertex property}} ==Definition== Suppose G is a connected undirected graph that has a finite [[defining ingredient::r..."

Vipul: Created page with "{{undirected graph vertex property}} ==Definition== Suppose $G$ is a connected undirected graph that has a finite [[defining ingredient::r..."