Intriguing sets in partial quadrangles

Abstract

We study intriguing sets in partial quadrangle

Weighted intriguing sets of finite generalised quadrangles

“…From the perspective of partial quadrangles, the following problem arose in [1]. Suppose G = (P, L) is a generalised quadrangle of order (s, s 2 ) and let p be a point of G. If we consider the set P p of points not collinear with p and the set of lines not incident with p, we produce a partial quadrangle PQ(G).…”

“…Suppose G = (P, L) is a generalised quadrangle of order (s, s 2 ) and let p be a point of G. If we consider the set P p of points not collinear with p and the set of lines not incident with p, we produce a partial quadrangle PQ(G). The point graph of PQ(G) has eigenvalues and multiplicities listed below in Table 2 (see [1]). …”

“…For the rest of the section, we examine improvements of results of Sect. 5 of [1]. For instance, we have generalised [1, Lemma 5.6] …”

“…1 Let be a line of a finite thick generalised quadrangle G of order (s, t) and let T be a group of automorphisms fixing and its concurrent lines (in the action on lines). Let m be a line concurrent but not equal to and consider the s points of m not on .…”

Intriguing Sets of Points of Q(2n, 2) \Q +(2n − 1, 2)

“…Intriguing sets of vertices have been studied for several classes of strongly regular graphs which arise as collinearity graphs of point-line geometries, see [3], [11] and [12] for generalized quadrangles, [2] for polar spaces, [7] for half-spin geometries and [1] for partial quadrangles. In the present paper, we study the intriguing sets of another class of strongly regular graphs.…”