On Resolvability of a Graph Associated to a Finite Vector Space

Usman Ali, Syed Ahtisham Bokhary, Khola Wahid

Published 2016-03-08Version 1

The metric dimension of non-component graph $\Gamma(\mathbb{V})$ on $n$-dimensional vector space $\mathbb{V}$ over a finite field $\mathbb{F}$ is determined. It is showed that the exchange property holds for resolving sets of the graph, except when the cardinality of $\mathbb{F}$ is $2$ and dimension of $\mathbb{V}$ is $\geq 3$. Some results are also related to an intersection graph.