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2012-05-29T03:34:08Z

Created page with "{{undirected graph property}} ==Definition== An undirected graph <math>G</math> is termed a '''distance-transitive graph''' if the following is true for every positive i..."

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{{undirected graph property}}

==Definition==

An [[undirected graph]] <math>G</math> is termed a '''distance-transitive graph''' if the following is true for every positive integer <math>i</math>: given vertices <math>v,w</math> of <math>G</math> at distance <math>i</math> from each other and vertices <matH>x,y</math> of <math>G</math> also at distance <math>i</math> from each other, there is a [[graph automorphism]] of <math>G</math> that sends <math>v</math> to <math>x</math> and <math>w</math> to <math>y</math>.

==Relation with other properties==

===Weaker properties===

{| class="sortable" border="1"
! Property !! Meaning !! Proof of implication !! Proof of strictness (reverse implication failure) !! Intermediate notions
|-
| [[Stronger than::symmetric graph]] || automorphism group is transitive on ordered pairs of adjacent vertices || || || {{intermediate notions short|symmetric graph|distance-transitive graph}}
|-
| [[Stronger than::edge-transitive graph]] || automorphism group is transitive on the edge set || || || {{intermediate notions short|edge-transitive graph|distance-transitive graph}}
|-
| [[Stronger than::vertex-transitive graph]] || automorphism group is transitive on the vertex set || || || {{intermediate notions short|vertex-transitive graph|distance-transitive graph}}
|-
| [[Stronger than::regular graph]] || all vertices have the same [[degree of a vertex|degree]] || || || {{intermediate notions short|regular graph|distance-transitive graph}}
|}

Distance-transitive graph - Revision history

Vipul: Created page with "{{undirected graph property}} ==Definition== An undirected graph G is termed a '''distance-transitive graph''' if the following is true for every positive i..."

Vipul: Created page with "{{undirected graph property}} ==Definition== An undirected graph $G$ is termed a '''distance-transitive graph''' if the following is true for every positive i..."