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
Mathematical Subject Classification 2010
Primary: 05C25
Supplementary material

Classification 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
Authors
Heather A. Newman
Department of Mathematics
Princeton University
Princeton, NJ
United States
Hector Miranda
Department of Mathematics
Lehigh University
Bethlehem, PA
United States
Adam Gregory
Department of Mathematics
University of Florida
Gainesville, FL
United States
Darren A. Narayan
School of Mathematical Sciences
Rochester Institute of Technology
Rochester, NY
United States