Is it true:
there is a simple planar graph $G$ with
minimum degree $4$,
each $2$ vertices of degree $4$ are nonadjacent
$G$ has no vertices of degree $5$.
Is it true:
there is a simple planar graph $G$ with
minimum degree $4$,
each $2$ vertices of degree $4$ are nonadjacent
$G$ has no vertices of degree $5$.
There are infinitely many such graphs. Have fun ;-)