2025/04/28 by Antonio Cossidente, Jan De Beule, Cossidente, Antonio +7 · 1 citation
Computer Science · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Matrix Theory and Algorithms #Primary 51E20 #Secondary 05E30
paper · pdf · doi:10.48550/arxiv.2504.19560
openalex publication_date 2025/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let Q+(2n+1,q) be a hyperbolic quadric of \PG(2n+1,q). Fix a generator Π of the quadric. Define \cGn as the graph with as vertex set the points of Q+(2n+1,q)∖ Π and two vertices adjacent if they either span a secant to Q+(2n+1,q) or a line contained in Q+(2n+1,q) meeting Π non-trivially. Then such a construction defines a strongly regular graph, which is the complement of a (non-induced) subgraph of the collinearity graph of Q+(2n+1,q). In this paper, we directly compute the parameters of \cGn, which is cospectral, when q=2, to the tangent graph NO+(2n+2,2), but it is non-isomorphic for n≥3. We also classify the maximal cliques of \cG3 for q=2, proving as a by-product the non-isomorphism with the graph NO+(8,2).