In mathematics, an arc-transitive graph is a graph G such that, given any two edges e1 = u1v1 and e2 = u2v2 of G, there are two automorphisms
- f : G → G, g : G → G
such that
- f (e1) = e2, g (e1) = e2
and
- f (u1) = u2, f (v1) = v2,
- g (u1) = v2, g (v1) = u2.
In other words, a graph is arc-transitive if its automorphism group acts transitively upon its arcs.
Related articles - Algebraic graph theory, Graph families
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- Arc-transitive graph
- Fri, 20 Mar 2009 05:57:03 GMT - girdle. In mathematics, an arc-transitive graph is a graph G such that, given any two edges e1 = u1v1 and e2 = u2v2 of G, there are two automorphisms. such that. and. In other words, a graph is arc-transitive if its automorphism group ...
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- Sun, 23 Sep 2007 23:37:00 GMT - The transitive closure of all the objects reachable by following the references from some root object is commonly called the object graph of the root object. Any object can be considered as the "root" of an object graph—although each object considered as ... A named object reference, just like an arc in a graph, represents (or "models") an arity-2 predicate, where the two nodes are the arguments of the predicate. The existence of the arc connecting the two graph nodes is, ...
Related resources:
Arc-transitive graph - tutorial aa
