If $\ X\ $ is a set, we let $\ \binom X2\,=\, \big\{\{a,b\}: a \neq b \in X \big\}.\ $ Given a simple, undirected graph $\ G=(V,E),\ $ we let $\ \delta(G)\ $ be its minimum degree, and $\ \Delta(G)\ $ its maximum degree. We say that $\ G\ $ is self-complementary if $\ G \cong \bar{G}\ $ where $\ \bar{G} = \left(V, \binom V2\setminus E\right)$.

Given $\ N\in\mathbb{N},\ $ is there a self-complimentary graph $\ G\ $ with $\ \Delta(G) \geq N\cdot \delta(G)\,$?