### Edge Regular Graph Products

#### Abstract

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.#### Keywords

Edge regular graph; graph products