Directed Graphs and Their Properties

The video tutorial introduces directed graphs, also known as digraphs, and explains their significance in modeling situations where direction is important. It compares undirected and directed graphs, defines directed edges and arcs, and discusses walks and paths in digraphs. The tutorial also covers the concepts of in-degree and out-degree of vertices, distinct arcs, and cycles in digraphs. Finally, it touches on the idea of connectedness in digraphs and introduces related theorems.

What is another name for directed graphs?

• Planar graphs

• Weighted graphs

• Bipartite graphs

• Digraphs

Why might we use directed graphs instead of undirected graphs?

• To simplify graph structures

• To model situations where direction is important

• To increase the number of vertices

• To represent relationships without direction

In an undirected graph, how is an edge defined?

• As a two-element subset

• As an ordered pair

• As a single vertex

• As a loop

What is the term used for directed edges in a digraph?

• Loops

• Cycles

• Paths

• Arcs

How is a directed edge represented in a digraph?

• As a two-element subset

• As a single vertex

• As an ordered pair

• As a loop

What is a walk in a directed graph?

• A sequence of vertices and edges

• A disconnected path

• A single vertex

• A loop

In a directed graph, what is the in-degree of a vertex?

• Number of edges entering the vertex

• Total number of vertices

• Number of loops

• Number of edges leaving the vertex

What is the out-degree of a vertex in a directed graph?

• Number of edges leaving the vertex

• Total number of vertices

• Number of loops

• Number of edges entering the vertex

What distinguishes arcs in a digraph?

• They are always bidirectional

• They form loops

• They are distinct and ordered

• They are unordered

What is a cycle in a directed graph?

• A path that starts and ends at the same vertex

• A sequence of disconnected vertices

• A single vertex

• A loop