Editing Edge-transitive graph (section)

{{short description|Graph where all pairs of edges are automorphic}}
{{about|graph theory|edge transitivity in geometry|Edge-transitive}}
{{Graph families defined by their automorphisms}}

In the [[mathematics|mathematical]] field of [[graph theory]], an  '''edge-transitive graph''' is a [[Graph (discrete mathematics)|graph]] {{mvar|G}} such that, given any two edges {{math|''e''{{sub|1}}}} and {{math|''e''{{sub|2}}}} of {{mvar|G}}, there is an [[Graph automorphism|automorphism]] of {{mvar|G}} that [[Map (mathematics)|maps]] {{math|''e''{{sub|1}}}} to {{math|''e''{{sub|2}}}}.<ref name="biggs">{{cite book | author=Biggs, Norman | title=Algebraic Graph Theory | edition=2nd | location=Cambridge | publisher=Cambridge University Press | year=1993 | page=118 | isbn=0-521-45897-8}}</ref>

In other words, a graph is edge-transitive if its [[automorphism group]] acts [[Group action#Remarkable properties of actions|transitively]] on its edges.