https://hal.inria.fr/hal-00990476Bailey, Robert F.Robert F.BaileyDepartment of Mathematics and Statistics, [Regina, Saskatchewan] - UR - University of ReginaMeagher, KarenKarenMeagherDepartment of Mathematics and Statistics, [Regina, Saskatchewan] - UR - University of ReginaOn the metric dimension of Grassmann graphsHAL CCSD2012[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Inria Sophia Antipolis-MÃ©diterranÃ©e / I3s, Service Ist2014-05-13 15:38:592018-08-24 11:18:012014-05-13 16:18:30enJournal articleshttps://hal.inria.fr/hal-00990476/document10.46298/dmtcs.532application/pdf1The metric dimension of a graph Gamma is the least number of vertices in a set with the property that the list of distances from any vertex to those in the set uniquely identifies that vertex. We consider the Grassmann graph G(q)(n, k) (whose vertices are the k-subspaces of F-q(n), and are adjacent if they intersect in a (k 1)-subspace) for k \textgreater= 2. We find an upper bound on its metric dimension, which is equal to the number of 1-dimensional subspaces of F-q(n). We also give a construction of a resolving set of this size in the case where k + 1 divides n, and a related construction in other cases.