This graph theory question is quite tough but I have not been able to make much progress with it:

We will say that a. graph G is isomorphic to the graph 5 where {7(5) = V{G) and a?) = {{'U, 11:} : 1),! E V(),{v, in} $5 E(G)}. Prove that if the number of vertical in graph G is divided by 4, the remainder is not 2 or 3