Semi-symmetric graph
In mathematics, an semi-symmetric graph is a graph that is edge-transitive and regular, but not vertex-transitive.
In other words, a regular graph is semi-symmetric if its automorphism group acts transitively upon its edges but not upon its vertices.
It is an easy consequence of the definition that a semi-symmetric graph must be bipartite, and that its automorphism group must act transitively on each of the two sets of the bipartition.
Examples and properties
- Dragan Marušič and Aleksander Malnic have shown that the smallest cubic semi-symmetric graph is the Gray graph on 54 vertices.
See also
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