On the metric dimension of affine planes, biaffine planes and generalized quadrangles [article]

Daniele Bartoli, Tamás Héger, György Kiss, Marcella Takáts
2017 arXiv   pre-print
In this paper the metric dimension of (the incidence graphs of) particular partial linear spaces is considered. We prove that the metric dimension of an affine plane of order q≥13 is 3q-4 and describe all resolving sets of that size if q≥ 23. The metric dimension of a biaffine plane (also called a flag-type elliptic semiplane) of order q≥ 4 is shown to fall between 2q-2 and 3q-6, while for Desarguesian biaffine planes the lower bound is improved to 8q/3-7 under q≥ 7, and to 3q-9√(q) under
more » ... n stronger restrictions on q. We determine the metric dimension of generalized quadrangles of order (s,1), s arbitrary. We derive that the metric dimension of generalized quadrangles of order (q,q), q≥2, is at least {6q-27,4q-7}, while for the classical generalized quadrangles W(q) and Q(4,q) it is at most 8q.
arXiv:1706.06583v1 fatcat:u76t3oen5ffpjdhqtayovhydme