Strictly Deza line graphs

For a given graph $G$, its line graph $L(G)$ is a graph such that its vertices represent the edges of $G$ and two vertices are adjacent if and only if the corresponding edges of $G$ have exactly one common vertex. A $k$-regular graph of diameter 2 with $v$ vertices is called a strictly Deza graph with parameters $(v,k,b,a)$ if it is not strongly regular and any two vertices have either $a$ or $b$ common neighbors. We present a classification of strictly Deza graphs that are line graphs.