非本原强正则图的充分条件

The Sufficient Conditions of Imprimitive Strongly Regular Graph

设 G 是一个(n,k,α,c)-强正则图,(n,■,■,■)是它的补图。若它们的参数满足下列条件之一:1)k,n—1互素;2)k,■互素;3)α=k—1,那么 G 是非本原的。G 是非本原的当且仅当■=■或■=0.

Let G be a(n,k,a,c)-strongly regular graph,(n,■,■,■)be its complement graph.If its parameters satisfies one of the following condition:1)k and n-1 coprime;2)k and■coprime;3)a=k—1,then Gis imprimitive.G is imprimitive of and only if■=■or■=0.