Switching equivalence of strongly regular polar graphs

Időpont: 
2025. 04. 29. 10:30
Hely: 
H306
Előadó: 
Nagy Gábor Péter (SZTE, BME)

We investigate the two-graphs associated with strongly regular polar graphs that belong to three infinite classes. Specifically, we examine the strongly regular graph Γ(O±(2m,2)), which has vertices representing points of a nondegenerate hyperbolic or elliptic quadric Q±(2m1,2) in the projective space PG(2m1,2). The set of vertices for NO±(2m,2) is the complement of Q±(2m1,2). Additionally, we consider the vertices of the third graph NO±(2m+1,q), where q is even, which correspond to hyperplanes of PG(2m,q) that intersect the nondegenerate parabolic quadric in a nondegenerate hyperbolic or elliptic quadric.

Our main result is the proof of switching equivalence for the strongly regular polar graphs NO±(4m,2), NO(2m+1,4), and Γ(O(4m,2)) with an isolated vertex. We establish this by providing an analytic description for these graphs and their corresponding two-graphs.