Source: Tokyo J. of Math.
Volume 33, Number 1
We say that a regular graph $G$ of order $n$ and degree $r\ge 1$ (which is not the complete graph) is strongly regular if there exist non-negative integers $\tau$ and $\theta$ such that $|S_i\cap S_j| = \tau$ for any two adjacent vertices $i$ and $j$, and $|S_i\cap S_j| = \theta$ for any two distinct non-adjacent vertices $i$ and $j$, where $S_k$ denotes the neighborhood of the vertex $k$.
We say that a graph $G$ of order $n$ is walk regular if and only if its vertex deleted subgraphs $G_i = G\smallsetminus i$ are cospectral for $i = 1,2,\ldots ,n$.
We here establish necessary and sufficient conditions under which a walk regular graph $G$ which is cospectral to its complement $\overline G$ is strongly regular.
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