Intriguing sets of strongly regular graphs and their related structures

In this paper we outline a technique for constructing directed strongly regular graphs by using strongly regular graphs having a "nice" family of intriguing sets. Further, we investigate such a construction method for rank three strongly regular graphs having at most $45$ vertices. Finally, several examples of intriguing sets of polar spaces are provided

On some 2-tight sets of polar spaces

Let Pi be a finite polar space of rank n >= 2 fully embedded into a projective space Sigma. In this note, we determine all tight sets of Pi of the form (Sigma(1) boolean AND P) boolean OR (Sigma(2) boolean AND P), where P denotes the point set of Pi and Sigma(1), Sigma(2) are two mutually disjoint subspaces of Sigma. In this way, we find two families of 2-tight sets of elliptic polar spaces that were not described before in the literature