Graph Theory Vertex Problem Let $G$ be a graph of order $8$ with $V(G)=\{v_1, v_2,...,v_8\}$ such that deg $v_i=i$ for $1 \leq i \leq 7$. What is deg $v_8$.
Any help or hints would be greatly appreciated.

You must join $v_7$ with all other vertices.
After that, $v_1$ is already "fed up". What can you now say about $v_6$? What happens then to $v_2$? And so on.
