Directed Graphs and Adjacency Matrices

This video lecture introduces the concept of directed graphs, also known as diagraphs, which consist of vertices and directed edges. It explains how these graphs differ from traditional XY plane graphs and how they can be represented as sets of vertices and edges. The lecture also covers the concepts of walks and paths, highlighting the differences between them, and demonstrates how graphs can be represented using adjacency matrices, which provide a unique representation of the graph's structure.

What is the primary focus of a directed graph compared to a traditional graph?

• The color of the vertices

• The direction of edges between vertices

• The relationship between X and Y

• The size of the graph

In a directed graph, what are the points called that are connected by edges?

• Vertices

• Nodes

• Points

• Dots

How is an edge represented in a directed graph?

• As a single vertex

• As a pair of vertices

• As a line

• As a triangle

What is the significance of the order of vertices in a directed edge?

• It determines the color of the edge

• It determines the direction of the edge

• It determines the weight of the edge

• It has no significance

What does a binary relation in a directed graph represent?

• A relation from one vertex to another

• A connection between two graphs

• A loop within a single vertex

• A color pattern in the graph

How can every binary relation be visualized?

• As a table

• As a graph

• As a list

• As a sequence

What is a walk in a directed graph?

• A loop

• A sequence of edges that cannot repeat vertices

• A sequence of edges that can repeat vertices

• A single edge

How is the length of a walk determined in a directed graph?

• By the number of loops

• By the number of vertices

• By the number of colors

• By the number of edges

What distinguishes a path from a walk in a directed graph?

• A path is shorter than a walk

• A path cannot repeat vertices

• A path can repeat vertices

• A path is longer than a walk

What happens if you repeat a vertex in a path?

• It becomes a walk

• It remains a path

• It becomes a loop

• It becomes a cycle