This is a question on Graph Theory. The book says :
1) If $v$ is a vertex in $G$, then $G-v$ is the subgraph of $G$ obtained by deleting $v$ from $G$and deleting all edges in $G$ which contain $v$.
If a node is deleted, it can either give birth to $1$ or more subgraphs.
2) If $e$ is an edge in $G$, then $G-e$ is the subgraph of $G$ obtained by simply deleting the edge $e$ from $G$.
Does the 2nd point mean that if an edge $e$ is deleted from a graph $G$, we can obtain a minimum of $2$ sub-graphs? With one sub-graph($G_1$) consisting of one node of the deleted edge $e$ and the other sub-graph($G_2$) consisting of the other and the only node(trivial graph)?
Is my understanding correct? Because the book nowhere mentions this.