Eulerian and Hamiltonian Graphs · Medium problem

A graph has a clique on $\{1,2,3,4,5,6\}$ (all $15$ edges present among them), plus vertex $7$ joined only to $1$ and $2$, plus vertex $8$ joined only to $3$ and $4$ ($8$ vertices total). Among all pairs of NON-adjacent vertices, find the smallest value of $\deg(u)+\deg(v)$.