In graph theory, we study relationships between objects. These objects are called vertices (or nodes), and the relationships between them are represented by edges.

Understanding Directed Graphs and Edges

A graph can be either undirected or directed. The key difference lies in whether the relationship between two vertices has a direction.

• Undirected Graph: In an undirected graph, an edge between vertex A and vertex B simply indicates a connection. There's no direction specified. The edge (A, B) is the same as the edge (B, A).
• Directed Graph: In a directed graph, edges have a specific direction. An edge goes from one vertex to another. For example, an edge from vertex A to vertex B is different from an edge from vertex B to vertex A. These directed edges are often called arcs.

The question specifically asks about notation for an edge in a directed graph that points from vertex A to vertex B.

Notation for Edges in Graphs

Different types of graphs use different notations for their edges to clearly indicate whether the edge is directed or undirected.

• Undirected Edge Notation: For an undirected edge connecting vertex A and vertex B, the common notation is an unordered set, typically written as $\{A, B\}$. The use of curly braces indicates that the order does not matter; $\{A, B\}$ is the same as $\{B, A\}$.
• Directed Edge Notation: For a directed edge going from vertex A to vertex B, the standard notation uses parentheses to denote an ordered pair. This is written as $(A, B)$. This notation explicitly states that the edge starts at the first element in the pair (A) and ends at the second element (B). Therefore, in a directed graph, $(A, B)$ is not the same as $(B, A)$ unless there are separate edges in both directions.

Analyzing the Given Options

Let's look at the provided options for denoting an edge that points from vertex A to vertex B in a directed graph:

• (A, B): This notation represents an ordered pair where A is the starting point and B is the ending point. This is the standard way to denote a directed edge from A to B in a directed graph. This matches our understanding of ordered pairs representing direction.
• [A, B]: This notation is not standard in basic graph theory to represent an edge. It is sometimes used for intervals or other mathematical concepts, but not typically for graph edge notation.
• <A, B>: While angular brackets can sometimes denote ordered pairs in certain mathematical contexts, parentheses (A, B) are the widely accepted and standard notation for directed edges in graph theory. Using <A, B> is less common for general graph edge notation.
• {A, B}: This notation represents an unordered set. In graph theory, it is the standard way to denote an edge in an undirected graph, where the connection between A and B has no specific direction. It does not specify an edge pointing from A to B; it simply means A and B are connected.

Based on the standard conventions of graph theory, the notation that correctly represents a directed edge pointing from vertex A to vertex B in a directed graph is $(A, B)$. This ordered pair notation clearly indicates the direction of the connection from the first vertex to the second vertex.