  In this paper, we simplify the known switching theorem due to Bose and
Shrikhande as follows.
  Let $G=(V,E)$ be a primitive strongly regular graph with parameters
$(v,k,\lambda,\mu)$.
  Let $S(G,H)$ be the graph from $G$ by switching with respect to a nonempty
$H\subset V$.
  Suppose $v=2(k-\theta_1)$ where $\theta_1$ is the nontrivial positive
eigenvalue of the $(0,1)$ adjacency matrix of $G$. This strongly regular graph
is associated with a regular two-graph.
  Then, $S(G,H)$ is a strongly regular graph with the same parameters if and
only if the subgraph induced by $H$ is $k-\frac{v-h}{2}$ regular. Moreover,
$S(G,H)$ is a strognly regualr graph with the other parameters if and only if
the subgraph induced by $H$ is $k-\mu$ regular and the size of $H$ is $v/2$. We
prove these theorems with the view point of the geometrical theory of the
finite set on the Euclidean unit sphere.

Combinatorics