\] Let $\Lambda, \Xi \subset \Gamma$ be two subgraphs and let $g,h \in \Gamma \mathcal{G}$ be two elements. Fix two vertices $x \in g \langle \Lambda \rangle$ and $y \in h \langle \Xi \rangle$ minimising the distance between $g\langle \Lambda \rangle$ and $h\langle \Xi \rangle$. 