On the metric dimension of incidence graph of M\"obius planes

Abstract

We study the metric dimension and optimal split-resolving sets of the point-circle incidence graph of a M\"obius plane. We prove that the metric dimension of a M\"obius plane of order $q$ is around $2q$, and that an optimal split-resolving set has cardinality between approximately $5q$ and $2.5q\log q$. We also prove that a smallest blocking set of a M\"obius plane of order $q$ has at most $2q(1 + \log(q + 1))$ points.