On amply regular locally \(GQ(4, 6)\)-graphs
An undirected \(k\)-regular graph with \(v\) vertices is called an amply regular graph with parameters \((v, k, \lambda, \mu)\) if any two adjacent vertices have exactly \(\lambda\) common neighbours and any two vertices of distance 2 apart have exactly \(\mu\) common neighbours. In an incidence structure \((P, {\mathcal B})\) (without multiple blocks) with point set \(P\) and block set \({\mathcal B}\), if any two blocks intersect in at most one point, then the blocks are called lines and the geometry \((P, {\mathcal B})\) is called a partial space. A partial space of order \((s, t)\) (that is, each line contains precisely \(s+1\) points and each point lies on precisely \(t+1\) lines) is called a generalised quadrangle, denoted \(GQ(s,t)\), if any antiflag \((a, L)\) there is a unique line containing \(a\) and intersecting \(L\).
scientific article; zbMATH DE number 6106457