We define the distance $d(a,\,b)$ between two vertices $a$ and $b$ of a graph as the least number of edges in a path from $a$ to $b.$ If no such path exists, then $d(a,\,b)=\infty.$ ... $\nu_G$ is the vocabulary of graphs.
(b) Does there exist a $\nu_G-$formula $\delta_{\infty}(a,\,b)$ so that, for any graph $G$, $G\models\delta_{\infty}(a,\,b)$ if and only if $d(a,\,b)=\infty$? Explain your answer.