Graph theory MOC

Graph automorphism

Let be a general graph. A graph automorphism is a bijection which leaves the adjacency matrix of fully invariant, #m/def/graph i.e.

for all . Clearly forms a group under composition, which in addition to an action on has an action on . A digraph is called

• vertex-transitive iff acts transitively on ;
• arc-transitive iff acts transitively on .

Results

• Every arc-transitive digraph is an orbital digraph

#state/tidy | #lang/en | #SemBr