Weakly Flag-transitive Configurations and Half-arc-transitive Graphs
A configuration is weakly flag-transitive if its group of automorphisms acts intransitively on flags but the group of all automorphisms and anti-automorphisms acts transitively on flags. It is shown that weakly flag-transitive configurations are in one-to-one correspondence with bipartite12-arc-tran...
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| Published in | European journal of combinatorics Vol. 20; no. 6; pp. 559 - 570 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Ltd
01.08.1999
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| Online Access | Get full text |
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| Summary: | A configuration is weakly flag-transitive if its group of automorphisms acts intransitively on flags but the group of all automorphisms and anti-automorphisms acts transitively on flags. It is shown that weakly flag-transitive configurations are in one-to-one correspondence with bipartite12-arc-transitive graphs of girth not less than 6. Several infinite families of weakly flag-transitive configurations are given via their Levi graphs. Among others an infinite family of non-self-polar weakly flag-transitive configurations is constructed. The smallest known weakly flag-transitive configuration has 27 points and the smallest known non-self-polar weakly flag-transitive configuration has 34 points. |
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| ISSN: | 0195-6698 1095-9971 |
| DOI: | 10.1006/eujc.1999.0302 |