tuple** $(v,k,\lambda,\mu)$ is defined to be a non-complete edge-regular graph with parameter tuple $(v,k,\lambda)$ such that every pair of non-adjacent vertices has precisely $\mu$ common neighbours. We refer to the elements of the parameter tuple as the **parameters** of $\Gamma$. We call the parameter tuple of a strongly regular graph **feasible** if its elements satisfy certain nonnegativity and divisibility constraints given by Brouwer [@CRCHAndbook2007 VII.11.5]). Let $\Gamma$ be a strongly regular graph with parameters $(v,k,\lambda,\mu)$. It is well-known that $\Gamma$ has at most three distinct eigenvalues, and moreover, the eigenvalues can be written in terms of the parameters of $\Gamma$ (see [@God01 Section 10.2]). In what follows we denote the eigenvalues of $\Gamma$ as $k > r \geqslant s$.

Strongly regular graphs whose parameters satisfy $k = (v-1)/2$, $\lambda = (v-5)/4$, and $\mu = (v-1)/4$ are called **type I** or **conference graphs**. Strongly regular graphs all of whose eigenvalues are integers are called **type II**. Every strongly regular graph is either type I, type II, or both type I and type II (see Cameron and Van Lint [@CvL Chapter 2]).

The **fractional part** of a real number $a \in \R$ is defined as ${\operatorname{frac} \left ( a \right )} := 