Another construction of edge-regular graphs with regular cliques

Gary R. W. Greaves, J. H. Koolen

Published 2018-10-17Version 1

We exhibit a new construction of edge-regular graphs with regular cliques that are not strongly regular. The infinite family of graphs resulting from this construction includes an edge-regular graph with parameters $(24,8,2)$. We also show that edge-regular graphs with $1$-regular cliques that are not strongly regular must have at least $24$ vertices.