yields True if the graph g is a vertex–transitive graph and False otherwise.
- A graph g is vertex transitive if for any vertices v and w of g, there is an automorphism of g that maps v to w.
- VertexTransitiveGraphQ is typically used to test whether all vertices in a graph have identical neighborhoods.
Examplesopen allclose all
Basic Examples (2)
VertexTransitiveGraphQ gives False for anything that is not a vertex–transitive graph:
VertexTransitiveGraphQ works with large graphs:
Generate a list of vertex–transitive graphs from GraphData:
Properties & Relations (7)
Every vertex–transitive graph is regular:
The graph complement of a vertex–transitive graph is vertex transitive:
Use GraphAutomorphismGroup to test whether a graph is vertex transitive:
Compute the orbit of a permutation group:
Single orbit should permute all vertices:
Use VertexTransitiveGraphQ to test whether a connected graph is edge transitive:
The edge connectivity of a vertex-transitive graph is equal to the degree :
The vertex connectivity of a vertex-transitive graph will be at least :
The vertex-transitive graph includes CompleteGraph:
Wolfram Research (2021), VertexTransitiveGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/VertexTransitiveGraphQ.html.
Wolfram Language. 2021. "VertexTransitiveGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/VertexTransitiveGraphQ.html.
Wolfram Language. (2021). VertexTransitiveGraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/VertexTransitiveGraphQ.html