# Metric dimension of imprimitive distance-regular graphs

### Robert Bailey Grenfell Campus, Memorial University

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Minisymposium: METRIC DIMENSION AND RELATED PARAMETERS

Content: The metric dimension of a graph \$\Gamma\$ is the least size of a set of vertices \$\{v_1, \ldots, v_m\}\$ with the property that, for any vertex \$w\$, the list of distances from \$w\$ to each of \$v_1, \ldots, v_m\$ uniquely identifies \$w\$. In this talk, we consider the metric dimension of imprimitive distance-regular graphs, which are either bipartite or antipodal (i.e. being at distance \$0\$ or \$d\$ is an equivalence relation on the vertices, where \$d\$ is the diameter). We use a theorem of Alfuraidan and Hall, along with the operations of ``halving'' and ``folding'', to reduce the problem to primitive graphs, where known results of Babai apply, except when the diameter is between \$3\$ and \$6\$. In this case, especially when the diameter is \$3\$, we see that unexpected things start to happen.

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