Graph Theory review

Front

What is a digraph in graph theory?

Back

A digraph (directed graph) is a graph where the edges have a direction, indicating a one-way relationship between vertices.

Front

Define vertices in the context of a graph.

Back

Vertices (or nodes) are the fundamental units of a graph, representing entities or points connected by edges.

Front

What is the degree of a vertex?

Back

The degree of a vertex is the number of edges connected to it. In a directed graph, it can be further classified into in-degree and out-degree.

Front

What does it mean for two vertices to be adjacent?

Back

Two vertices are adjacent if there is an edge connecting them.

Front

How do you represent a graph using a set of vertices and edges?

Back

A graph can be represented as G = (V, E), where V is the set of vertices and E is the set of edges connecting those vertices.

Front

What is the difference between a directed graph and an undirected graph?

Back

In a directed graph, edges have a direction, while in an undirected graph, edges do not have a direction and represent a two-way relationship.

Front

What is an example of a real-world application of graph theory?

Back

Graph theory is used in computer networks to model connections between devices, in social networks to analyze relationships, and in project management to represent tasks and dependencies.

Front

What is a path in a graph?

Back

A path is a sequence of edges that connects a sequence of vertices without revisiting any vertex.

Front

What is a cycle in a graph?

Back

A cycle is a path that starts and ends at the same vertex, with no other vertices repeated.

Front

Define a connected graph.

Back

A connected graph is a graph in which there is a path between every pair of vertices.