On the metric dimension of bilinear forms graphs

In [R.F. Bailey, K. Meagher, On the metric dimension of Grassmann graphs, arXiv:1010.4495], Bailey and Meagher obtained an upper bound on the metric dimension of Grassmann graphs. In this note we show that q n + d − 1 + ⌊ d + 1 n ⌋ is an upper bound on the metric dimension of bilinear forms graphs H q ( n , d ) when n ≥ d ≥ 2 . As a result, we obtain an improvement on Babai’s most general bound for the metric dimension of distance-regular graphs, in the case of H q ( n , d ) with n ≥ d ≥ 4 .