Vipul at 17:59, 28 May 2012

2012-05-28T17:59:49Z

← Older revision		Revision as of 17:59, 28 May 2012
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	\| [[Radius of a graph]] \|\| minimum of eccentricities of vertices \|\| Radius <math>\le</math> Diameter <math>\le</math> Twice the radius		\| [[Radius of a graph]] \|\| minimum of eccentricities of vertices \|\| Radius <math>\le</math> Diameter <math>\le</math> Twice the radius
	\|}		\|}

			==Related graph properties==

			* [[Graph of finite diameter]]
			* [[Graph of constant finite eccentricity]]

Vipul: Created page with "{{undirected graph numerical invariant}} ==Definition== The '''diameter of a graph''' is defined for any connected graph as the diameter of the [[metric space induced by..."

2012-05-28T17:59:09Z

Created page with "{{undirected graph numerical invariant}} ==Definition== The '''diameter of a graph''' is defined for any connected graph as the diameter of the [[metric space induced by..."

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{{undirected graph numerical invariant}}

==Definition==

The '''diameter of a graph''' is defined for any [[connected graph]] as the diameter of the [[metric space induced by a connected graph|metric space induced by it]]. Explicitly, for a graph <math>G</matH> with vertex set <math>V(G)</math>, it is:

<math>\max_{x \in V(G)} \left(\max_{y \in V(G)} d(x,y)\right)</math>

where <math>d</math> denotes the distance between two vertices. In words, the diameter of a graph is the maximum, over all vertices, of the [[eccentricity of a vertex|eccentricity of that vertex]].

Note that for a connected [[finite graph]], the diameter is finite. For an infinite connected graph, the diameter may be finite or <math>\infty</math>. A [[graph of finite diameter]] is a connected graph (finite or infinite) whose diameter is finite.

For a graph that is not connected, we can consider the diameter to be either <math>\infty</math> or undefined.

==Related invarants==

{| class="sortable" border="1"
! Invariant !! Meaning !! Relation with radius
|-
| [[Radius of a graph]] || minimum of eccentricities of vertices || Radius <math>\le</math> Diameter <math>\le</math> Twice the radius
|}

Diameter of a graph - Revision history

Vipul at 17:59, 28 May 2012

Vipul: Created page with "{{undirected graph numerical invariant}} ==Definition== The '''diameter of a graph''' is defined for any connected graph as the diameter of the [[metric space induced by..."