On critically 3-connected graphs with exactly two vertices of degree 3. Part 2

A graph $G$ is critically $3$-connected, if $G$ is $3$-connected and for any vertex $v\in V(G)$ the graph $G-v$ isn't $3$-connected. R. C. Entringer and P. J. Slater proved that any critically $3$-connected graph contains at least two vertices of degree $3$. In the previous paper we classify all such graphs with one additional condition: two vertices of degree $3$ are adjacent. In this paper we will consider the case of nonadjacent vertices of degree $3$.