Graph Terminology

Description: This quiz will test your understanding of the basic terminology used in graph theory.
Number of Questions: 15
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Tags: graph theory terminology
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What is a graph?

  1. A collection of vertices and edges

  2. A collection of vertices and arcs

  3. A collection of edges and arcs

  4. A collection of vertices, edges, and arcs


Correct Option: A
Explanation:

A graph is a mathematical structure consisting of a set of vertices and a set of edges, where each edge connects a pair of vertices.

What is a vertex?

  1. A point in a graph

  2. A line in a graph

  3. A curve in a graph

  4. A surface in a graph


Correct Option: A
Explanation:

A vertex is a point in a graph that represents an object or a concept.

What is an edge?

  1. A line in a graph

  2. A curve in a graph

  3. A surface in a graph

  4. A solid in a graph


Correct Option: A
Explanation:

An edge is a line in a graph that connects a pair of vertices.

What is a path?

  1. A sequence of vertices and edges

  2. A sequence of vertices

  3. A sequence of edges

  4. A sequence of vertices and arcs


Correct Option: A
Explanation:

A path is a sequence of vertices and edges that connects a pair of vertices.

What is a cycle?

  1. A path that starts and ends at the same vertex

  2. A path that starts and ends at different vertices

  3. A path that has no repeated vertices

  4. A path that has no repeated edges


Correct Option: A
Explanation:

A cycle is a path that starts and ends at the same vertex.

What is a tree?

  1. A connected graph with no cycles

  2. A connected graph with at least one cycle

  3. A disconnected graph with no cycles

  4. A disconnected graph with at least one cycle


Correct Option: A
Explanation:

A tree is a connected graph with no cycles.

What is a forest?

  1. A collection of trees

  2. A collection of cycles

  3. A collection of paths

  4. A collection of arcs


Correct Option: A
Explanation:

A forest is a collection of trees.

What is a connected graph?

  1. A graph in which every pair of vertices is connected by a path

  2. A graph in which every pair of vertices is connected by a cycle

  3. A graph in which every pair of vertices is connected by an edge

  4. A graph in which every pair of vertices is connected by an arc


Correct Option: A
Explanation:

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

What is a disconnected graph?

  1. A graph in which some pairs of vertices are not connected by a path

  2. A graph in which some pairs of vertices are not connected by a cycle

  3. A graph in which some pairs of vertices are not connected by an edge

  4. A graph in which some pairs of vertices are not connected by an arc


Correct Option: A
Explanation:

A disconnected graph is a graph in which some pairs of vertices are not connected by a path.

What is a complete graph?

  1. A graph in which every pair of vertices is connected by an edge

  2. A graph in which every pair of vertices is connected by a cycle

  3. A graph in which every pair of vertices is connected by a path

  4. A graph in which every pair of vertices is connected by an arc


Correct Option: A
Explanation:

A complete graph is a graph in which every pair of vertices is connected by an edge.

What is a subgraph?

  1. A graph that is contained in another graph

  2. A graph that is not contained in another graph

  3. A graph that is connected to another graph

  4. A graph that is disconnected from another graph


Correct Option: A
Explanation:

A subgraph is a graph that is contained in another graph.

What is a spanning subgraph?

  1. A subgraph that contains all of the vertices of the original graph

  2. A subgraph that contains all of the edges of the original graph

  3. A subgraph that contains all of the vertices and edges of the original graph

  4. A subgraph that contains none of the vertices or edges of the original graph


Correct Option: C
Explanation:

A spanning subgraph is a subgraph that contains all of the vertices and edges of the original graph.

What is a weighted graph?

  1. A graph in which each edge has a weight

  2. A graph in which each vertex has a weight

  3. A graph in which each path has a weight

  4. A graph in which each cycle has a weight


Correct Option: A
Explanation:

A weighted graph is a graph in which each edge has a weight.

What is a directed graph?

  1. A graph in which each edge has a direction

  2. A graph in which each vertex has a direction

  3. A graph in which each path has a direction

  4. A graph in which each cycle has a direction


Correct Option: A
Explanation:

A directed graph is a graph in which each edge has a direction.

What is an undirected graph?

  1. A graph in which each edge does not have a direction

  2. A graph in which each vertex does not have a direction

  3. A graph in which each path does not have a direction

  4. A graph in which each cycle does not have a direction


Correct Option: A
Explanation:

An undirected graph is a graph in which each edge does not have a direction.

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