#### Vol. 12, No. 8, 2019

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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
##### Abstract

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 $20$ 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.

##### Keywords
edge-transitive, combinatorial designs
Primary: 05C25
##### Supplementary material

Classification of connected edge-transitive graphs on 20 vertices or less