Item 4.7.5.b.

This is easy to do if you draw the picture. Here is such a graph:

$A tree with a bottom vertex adjacent to each of three vertices in a row above it. Each of these is adjacent to another vertex directly above them.$

Any labeling of this graph will be not isomorphic to $G\text{.}$ For example, we could take $V'' = \{a,b,c,d,e,f,g\}$ and $E'' = \{ab, ac, ad, be, cf, dg\} \text{.}$