Authors: Robert F. Bailey ^{1}; Karen Meagher ^{1}
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Robert F. Bailey;Karen Meagher
1 Department of Mathematics and Statistics, [Regina, Saskatchewan]
The 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.
Hayat, Sakander; Khan, Asad; Zhong, Yubin, 2022, On Resolvability- And Domination-Related Parameters Of Complete Multipartite Graphs, Mathematics, 10, 11, pp. 1815, 10.3390/math10111815.
Mladenović, Nenad; Kratica, Jozef; Kovačević-Vujčić, Vera; Čangalović, Mirjana, 2012, Variable Neighborhood Search For Metric Dimension And Minimal Doubly Resolving Set Problems, European Journal Of Operational Research, 220, 2, pp. 328-337, 10.1016/j.ejor.2012.02.019.