Let G,H be graphs and G?H represent a particular graph product of G H. We define im(G) to the largest t such that has Kt-immersion ask: given im(G)=t im(H)=r, how large is im(G?H)? Best possible lower bounds are provided when ? Cartesian or lexicographic product, conjecture offered for each direct strong products, along with some partial results.

A regular nonempty graph Γ is called edge regular, whenever there exists a nonegative integer λΓ, such that any two adjacent vertices of Γ have precisely λΓ common neighbours. An edge regular graph Γ with at least one pair of vertices at distance 2 is called amply regular, whenever there exists a nonegative integer μΓ, such that any two vertices at distance 2 have precisely μΓ common neighbours...