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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