Graph Theory Quiz

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.