What is a lobe in graph theory?

Question

I've tried googling it, but nothing really shows up. I ask because I'm reading a Lemma from Douglas West's Introduction to Graph Theory.

Let S = {x, y} be a separating 2-set of $G$. If $G$ is nonplanar, then adding the edge $xy$ to some $S$-lobe of $G$ yields a nonplanar graph.

I don't know what an $S$-lobe is.

Answer 1

Quoting from a flat text version of this book I found online:

"Note also that the proof uses the notion of S-lobe defined in Section 5.2."

"5.2.17. Definition. Let S be a set of vertices in a graph G. An S-lobe of G is an induced subgraph of G whose vertex set consists of S and the vertices of a component of G - S."

I'll leave understanding it to you, seen as I've not studied graph theory to that level presently. Hopefully that helps