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Edge-transitive
graphs and combinatorial designs
Heather A. Newman, Hector Miranda, Adam Gregory and Darren A. Narayan
Vol. 12 (2019), No. 8, 1329–1341
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Abstract |
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A graph is said to be edge-transitive if its automorphism group acts transitively on its edges. It is known that edge-transitive graphs are either vertex-transitive or bipartite. We present a complete classification of all connected edge-transitive graphs on less than or equal to vertices. We investigate biregular bipartite edge-transitive graphs and present connections to combinatorial designs, and we show that the Cartesian products of complements of complete graphs give an additional family of edge-transitive graphs. |
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Keywords
edge-transitive, combinatorial designs
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Mathematical Subject Classification 2010
Primary: 05C25
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Supplementary materialClassification of connected edge-transitive graphs on 20 vertices or less |
Milestones
Received: 28 January 2019
Revised: 15 May 2019
Accepted: 10 June 2019
Published: 25 October 2019
Communicated by Anant Godbole
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Authors |
| Heather A. Newman | |
| Department of Mathematics Princeton University Princeton, NJ United States |
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| Hector Miranda | |
| Department of Mathematics Lehigh University Bethlehem, PA United States |
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| Adam Gregory | |
| Department of Mathematics University of Florida Gainesville, FL United States |
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| Darren A. Narayan | |
| School of Mathematical
Sciences Rochester Institute of Technology Rochester, NY United States |
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