On $K_{1,3}$-free strictly Deza graphs

A Deza graph with parameters $(v,k,b,a)$ is a $k$-regular graph with $v$ vertices where any two vertices have either $a$ or $b$ common neighbors. We describe strict Deza graphs that do not contain $K_{1,3}$ among their induced subgraphs and are unions of closed neighborhoods of two nonadjacent vertices. The latter condition means that there are two nonadjacent vertices such that any other vertex is adjacent to at least one of them.