Give a graph model for a permutation problem 
Describe a graph model for solving the following problem: Can the permutations of $\{1,2,\ldots,n\}$ be arranged in a sequence so that the adjacent permutations $$p:p_1,\ldots,p_n \text{ and }  q:q_1,\ldots,q_n$$ satisfy $p_i\neq q_i$ for all $i$?

I have problem understanding what the exercise asks. What does "adjacent permutation" mean? Also, in a follow-up question, it says that the statement is true for $n\geq 5$. 

I think they mean permutations that are adjacent in the sequence. If the sequence is $\pi_1,\pi_2,\ldots,\pi_{n!}$, then e.g. $\pi_5$ and $\pi_6$ would be adjacent. And where it says "the adjacent permutations" I think they mean "any two adjacent permutations".
