Abstract: We present simple, geometric constructions for small regular graphs of girth 7 from the incidence graphs of some generalized quadrangles. We obtain infinite families of (q − 1)-regular, q-regular and (q + 1)-regular graphs of girth 7, for q a prime power. Some of them have the smallest order known so far.Keywords: cage problem, incidence graph, generalized quadranglePublished in RUP: 03.11.2025; Views: 326; Downloads: 1 Full text (392,97 KB)
Keywords: (near-) linear space, projective plane, affine plane, partial geometry, generalized quadrangle, strongly regular graph, partial difference set, automorphism groupPublished in RUP: 25.12.2024; Views: 1869; Downloads: 31 Full text (1,22 MB)
