  A nonempty $k$-regular graph $\Gamma$ on $n$ vertices is called a Deza graph
if there exist constants $b$ and $a$ $(b \geq a)$ such that any pair of
distinct vertices of $\Gamma$ has precisely either $b$ or $a$ common
neighbours. The quantities $n$, $k$, $b$, and $a$ are called the parameters of
$\Gamma$ and are written as the quadruple $(n,k,b,a)$. If a Deza graph has
diameter 2 and is not strongly regular, then it is called a strictly Deza
graph. In the paper we investigate strictly Deza graphs with parameters $ (n,
k, b, a) $, where its quantities satisfy the conditions $k = b + 1$ and
$\frac{k(k - 1) - a(n - 1)}{b - a} > 1$.
