EdgeTransitiveGraphQ

EdgeTransitiveGraphQ[g]

yields True if the graph g is a edge-transitive graph and False otherwise.

Details

  • A graph g is edge transitive if for any edges e1 and e2 of g, there is an automorphism of g that maps e1 to e2.
  • EdgeTransitiveGraphQ is typically used to test whether all edges in a graph have identical neighborhoods.

Examples

open allclose all

Basic Examples  (2)

Test whether a graph is edge transitive:

A wheel graph is not edge transitive:

Scope  (7)

Test undirected graphs:

Directed graphs:

Multigraphs:

Mixed graphs:

Tagged graphs:

EdgeTransitiveGraphQ gives False for anything that is not an edge-transitive graph:

EdgeTransitiveGraphQ works with large graphs:

Applications  (1)

Generate a list of edge-transitive graphs from GraphData:

Check:

Properties & Relations  (5)

Connected edge-transitive graphs are either vertex transitive or bipartite:

Use VertexTransitiveGraphQ to test whether a connected graph is edge transitive:

THe edge-transitive graphs need not be vertex transitive:

The vertex connectivity of an edge-transitive graph equals its minimum degree:

The edge-transitive graph includes CompleteGraph:

Complete bipartite graph:

CycleGraph:

Gray graph:

Wolfram Research (2021), EdgeTransitiveGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeTransitiveGraphQ.html.

Text

Wolfram Research (2021), EdgeTransitiveGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/EdgeTransitiveGraphQ.html.

CMS

Wolfram Language. 2021. "EdgeTransitiveGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EdgeTransitiveGraphQ.html.

APA

Wolfram Language. (2021). EdgeTransitiveGraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EdgeTransitiveGraphQ.html

BibTeX

@misc{reference.wolfram_2024_edgetransitivegraphq, author="Wolfram Research", title="{EdgeTransitiveGraphQ}", year="2021", howpublished="\url{https://reference.wolfram.com/language/ref/EdgeTransitiveGraphQ.html}", note=[Accessed: 21-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_edgetransitivegraphq, organization={Wolfram Research}, title={EdgeTransitiveGraphQ}, year={2021}, url={https://reference.wolfram.com/language/ref/EdgeTransitiveGraphQ.html}, note=[Accessed: 21-December-2024 ]}