Resolving Sets and Split Resolving Sets of Symmetric Designs - Beke, Ákos (The Electronic Journal of Combinatorics, 2026)
We study resolving sets and split resolving sets of the point-block incidence graphs of symmetric designs and we obtain general lower bounds on their cardinality. In some cases, this lower bound is just a constant factor away from the known upper bounds. In particular, we show that for any ε>0 there exists q_0 and n_0 such that if q≥ q_0 and n≥ n_0, then the metric dimension of the point-hyperplane incidence graph of PG(n,q) is at least (2-ε)nq. The best known upper bound for the metric dimension of PG(n,q) is roughly 4nq. We also prove that the metric dimension of a symmetric (v,k,λ) design, under certain conditions, is at least (2-ε)uvk for any ε >0, where u=vv - k +1floor.