Graph G =(V,E) contains two vertices of degree 1 and, for every k∈2,...,n−1, exactly one vertex of degree k. Show that n cannot be a multiple of 4. Let $G = (V, E)$ be a simple undirected graph of n vertices.
Suppose that $G$ contains two vertices of degree 1 and, for every $k ∈ \{2, . . . , n − 1\}$, exactly one vertex of degree $k$. Show that $n$ cannot be a multiple of 4.
I tried to use the degree-vertex relation but didn't help. 
$$\sum deg(v) = 2 |E|$$

Using the degree-vertex property
$$\sum deg(v) = 1 + 2 + 3 +... +n-1 + 1 = 1 + \frac{(n-1)(n)}{2}$$
Now, if $n$ is a multiple of 4, then this sum is odd, which is not possible as it must be equal to $2|E|$
