Biprimitive graphs of smallest order (Q1283454)
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scientific article; zbMATH DE number 1275696
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Biprimitive graphs of smallest order |
scientific article; zbMATH DE number 1275696 |
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Biprimitive graphs of smallest order (English)
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13 April 1999
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A regular edge-transitive graph which is not vertex-transitive is called a semisymmetric graph. A semisymmetric graph is necessarily bipartite, with the two parts having equal size and the automorphism group acting transitively on the vertices of each part. A semisymmetric graph is biprimitive if the action of the automorphism group on each part is primitive. The authors show that the smallest order for which a biprimitive graph exists is 80 and there are exactly two such graphs, one of valency 4 and the other of valency 36.
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semisymmetric graph
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automorphism group
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biprimitive graph
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