Graph Theory Quiz

Study Notes

Graph Components

A graph consists of vertices (or nodes) and edges (connections between vertices).
Vertices represent entities or points, while edges represent relationships or connections.

Edge in a Graph

An edge is a connection linking two vertices in a graph.
Edges can be directed (indicating a one-way relationship) or undirected (indicating a two-way relationship).

Regular Graph

A regular graph is one where each vertex has the same degree, meaning every vertex has the same number of edges.
Regular graphs provide uniformity and are important in various applications like network design.

Bipartite Graph

A bipartite graph is structured with two distinct sets of vertices, where edges only connect vertices from different sets, not within the same set.
Used for modeling relationships in problems like matchmaking and job assignments.

Complete Graph

A complete graph is one in which every pair of distinct vertices is connected by a unique edge.
Denoted as K_n, where n is the number of vertices; includes a maximum number of edges.

Vertex in a Graph

A vertex (or node) is a fundamental unit of a graph representing an entity or point.
Vertices are often labeled and can have associated data or attributes.

Degree of a Vertex

The degree of a vertex refers to the number of edges connected to it.
In directed graphs, there are in-degrees (edges coming into the vertex) and out-degrees (edges going out from the vertex), providing insight into the vertex's connectivity.

Description

Test your knowledge of graph theory with this quiz covering topics such as types of graphs, vertex degree, complete and regular graphs, cycles, bipartite graphs, and more. This quiz is a great way to review and reinforce your understanding of graph theory concepts.