Graph Theory

Graph Theory

University

10 Qs

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Graph Theory

Graph Theory

Assessment

Quiz

Mathematics

University

Practice Problem

Hard

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10 questions

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1.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the following is the correct formal definition of a graph?

A collection of equations and inequalities

A structure consisting of a set of vertices and a set of edges connecting them

A function from vertices to numbers

A sequence of numbers arranged in a table

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What distinguishes a simple graph from a directed graph?

A simple graph can have loops, while a directed graph cannot

A simple graph has directions on edges, while a directed graph does not.

A simple graph has undirected edges with no loops or multiple edges; a directed graph has edges with direction

There is no difference

3.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the following diagrams represents a complete graph on 4 vertices?

Media Image
Media Image
Media Image

None of the above

4.

OPEN ENDED QUESTION

1 min • 1 pt

True or False: In a bipartite graph, each edge connects a vertex from one subset to a vertex in the same subset.

Evaluate responses using AI:

OFF

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Media Image

In the graph shown, what is the degree of vertex B?

2

3

4

5

6.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

The graph is connected and has four vertices of even degree. What can we conclude?

It has an Eulerian circuit

It has an Eulerian path but not a circuit

It is a bipartite graph

It cannot be traversed in one path

7.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Which of the following statements about Hamiltonian paths is TRUE?

A Hamiltonian path visits every edge exactly once

A Hamiltonian path must begin and end at the same vertex

A Hamiltonian path visits every vertex exactly once

A Hamiltonian path only exists in complete graphs

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