Isolated Vertices, Leaves, and Pendant Edges
Table of Contents

Isolated Vertices, Leaves, and Pendant Edges
Isolated Vertices
Definition: For a graph $G = (V(G), E(G))$, a vertex $x_1 \in V(G)$ is considered Isolated if $\mathrm{deg} (x_1) = 0$. 
For example, the following graph has one isolated vertex:
Note that if a graph has an isolated vertex, then the graph is disconnected.
Leaves
Definition: For a graph $G = (V(G), E(G))$, a vertex $x_1 \in V(G)$ is considered a Leaf if $\mathrm{deg} (x_1) = 1$. 
For example, the following graph has one leaf, namely the vertex labelled "$1$":
Pendant Edge
Definition: For a graph $G = (V(G), E(G))$, an edge connecting a leaf is called a Pendant Edge. 
From the example earlier, we can highlight the pendant edge of the graph: