Vipul: Created page with "{{undirected graph property}} ==Definition== An undirected graph is termed a '''symmetric graph''', '''arc-transitive graph''', or '''flag-transitive graph''' either if ..."

2012-05-28T03:21:39Z

Created page with "{{undirected graph property}} ==Definition== An undirected graph is termed a '''symmetric graph''', '''arc-transitive graph''', or '''flag-transitive graph''' either if ..."

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{{undirected graph property}}

==Definition==

An [[undirected graph]] is termed a '''symmetric graph''', '''arc-transitive graph''', or '''flag-transitive graph''' either if it is the [[empty graph]] or the induced action of the [[automorphism group of a graph|automorphism group]] on the set of ordered pairs of adjacent vertices is [[groupprops:transitive group action|transitive]].

==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::empty graph]] || || || ||
|-
| [[Weaker than::complete graph]] || || || ||
|}

===Weaker properties===

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

Symmetric graph - Revision history

Vipul: Created page with "{{undirected graph property}} ==Definition== An undirected graph is termed a '''symmetric graph''', '''arc-transitive graph''', or '''flag-transitive graph''' either if ..."