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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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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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