On pseudofrobenius imprimitive association schemes

An (association) scheme is said to be Frobenius if it the (orbital) of a group. A which has same tensor intersection numbers as some pseudofrobenius. We establish necessary and sufficient condition for an imprimitive pseudofrobenius Frobenius. also prove strong conditions existence not As byproduct, we obtain group G with abelian kernel determined up isomorphism only by character table G. Finally, that Weisfeiler-Leman dimension circulant graph n vertices automorphism equal 2 unless $$n\in \{p,p^2,p^3,pq,p^2q\}$$ , where p q are distinct primes.