Edge regular graph products (Q1953451)

Summary: A regular nonempty graph \(\Gamma\) is called edge regular, whenever there exists a nonegative integer \(\lambda_{\Gamma}\), such that any two adjacent vertices of \(\Gamma\) have precisely \(\lambda_{\Gamma}\) common neighbours. An edge regular graph \(\Gamma\) with at least one pair of vertices at distance 2 is called amply regular, whenever there exists a nonegative integer \(\mu_{\Gamma}\), such that any two vertices at distance 2 have precisely \(\mu_{\Gamma}\) common neighbours. In this paper we classify edge regular graphs, which can be obtained as a strong product, or a lexicographic product, or a deleted lexicographic product, or a co-normal product of two graphs. As a corollary we determine which of these graphs are amply regular.