What is meant by a graph $G$ of order $n$ being strongly regular with parameters $(d, a, b) ?$ Show that, if such a graph $G$ exists and $b>0$, then

$$\frac{1}{2}\left\{n-1+\frac{(n-1)(b-a)-2 d}{\sqrt{(a-b)^{2}+4(d-b)}}\right\}$$

is an integer.

Let $G$ be a graph containing no triangles, in which every pair of non-adjacent vertices has exactly three common neighbours. Show that $G$ must be $d$-regular and $|G|=1+d(d+2) / 3$ for some $d \in\{1,3,21\}$. Show that such a graph exists for $d=3$.