Cutting-edge Graph Theory Test - 68+ MCQs: Graph Theory test: Challenge Your Knowledge with Graph Theory Questions and Answers

1. Which of the following properties does a complete bipartite graph possess?

All vertices on one side are connected to all vertices on the other side

All vertices on one side are connected to some vertices on the other side

There are no edges between vertices on the same side

Every vertex is connected to every other vertex

2. What is the term used for a graph in which there is an edge between every pair of vertices?

Tree

Cycle

Complete Graph

Bipartite Graph

3. What is the term used for a graph that has exactly one vertex of odd degree?

Eulerian Graph

Hamiltonian Graph

Semi-Eulerian Graph

Bipartite Graph

4. Which graph theory problem involves finding the shortest path from a source vertex to all other vertices in a weighted graph?

Hamiltonian Path Problem

Eulerian Path Problem

Dijkstra's Algorithm

Kruskal's Algorithm

5. Which of the following properties does a graph possess if it can be drawn in such a way that no edges intersect each other?

Connected Graph

Planar Graph

Cyclic Graph

Complete Graph

6. What is the edge chromatic number of a complete graph with 'n' vertices?

n-1

n/2

7. What does the term 'adjacent' mean in the context of graph theory?

Two vertices connected by an edge

Two edges connected by a vertex

Two vertices without any connection

Two edges without any vertex in common

8. What is the maximum number of edges in a simple graph with 5 vertices?

9. Which theorem states that the sum of the degrees of all vertices in a graph is twice the number of edges?

Euler's Theorem

Handshaking Lemma

Königsberg's Theorem

Hamilton's Theorem

10. Which of the following is true about a tree?

It has exactly one cycle

It has no cycles

It has exactly two cycles

It has more than two cycles

11. In graph theory, what does a perfect matching in a graph mean?

A matching that covers all the vertices

A matching that covers half of the vertices

A matching with the maximum number of edges

A matching with the minimum number of edges

12. Which theorem states that every connected finite simple graph with at least two vertices has a vertex of degree at most 1?

Dirac's Theorem

Euler's Theorem

Konig's Theorem

Turan's Theorem

13. What is the term used for a path in a graph that starts and ends at the same vertex and visits every vertex exactly once?

Hamiltonian Path

Eulerian Path

Knight's Tour

Cycle

14. Which of the following statements about Eulerian graphs is true?

Every vertex has an even degree.

There is a path that visits every edge exactly once.

There is a cycle that visits every vertex exactly once.

It is possible to color the vertices with two colors such that no two adjacent vertices have the same color.

15. In graph theory, what does a 'cut edge' refer to?

An edge that increases the number of connected components when removed

An edge that decreases the number of connected components when removed

An edge that doesn't affect the graph when removed

An edge that splits the graph into two equal parts

16. What is the term used for a graph in which the edges have a direction?

Undirected Graph

Bipartite Graph

Directed Graph

Multigraph

17. Which of the following properties does a bipartite graph possess?

All vertices can be colored with the same color

Vertices can be partitioned into two sets such that no edge connects vertices from the same set

There is a path between every pair of vertices

Every vertex is connected to every other vertex

18. What does a spanning tree of a connected graph mean?

A tree that spans the graph and includes all vertices

The largest tree in a graph

A tree with the most branches

The smallest tree in a graph

19. Which of the following is a property of a planar graph?

It can be drawn without any edges crossing.

It has a Hamiltonian cycle.

It has a chromatic number of 3.

It has an Eulerian path.

20. Which theorem states that if every vertex of a graph has even degree, then the graph has a closed Eulerian trail?

Euler's Theorem

Handshaking Lemma

Pigeonhole Principle

Strong Connectivity Theorem

21. What does the matrix tree theorem relate to in graph theory?

Number of spanning trees

Chromatic number

Connectivity

Cycle detection

22. Which of the following is a graph with vertices divided into two disjoint sets such that every edge connects a vertex in one set to a vertex in the other set?

Complete Graph

Tree

Bipartite Graph

Cyclic Graph

23. Which graph theory problem involves finding a subgraph that is both a tree and a spanning subgraph of a given graph?

Hamiltonian Cycle Problem

Eulerian Path Problem

Minimum Spanning Tree Problem

Bipartite Matching Problem

24. What is the term used for a cycle in a directed graph that traverses each edge exactly once?

Hamiltonian Cycle

Eulerian Cycle

Knight's Tour

Cycle Cover

25. What is the maximum number of edges in an acyclic graph with 'n' vertices?

n-1

n/2

26. In graph theory, what does 'path' refer to?

A connected subgraph without cycles

A collection of vertices

A collection of edges

A set of nodes without any edges

27. What is the term used for a subgraph that contains all the vertices of the original graph and is also a tree?

Cut Tree

Minimal Spanning Tree

Maximal Spanning Tree

Steiner Tree

28. Which of the following is a graph with no cycles and has at most one edge between any two vertices?

Bipartite Graph

Cyclic Graph

Simple Graph

Directed Graph

29. What is the basic definition of a graph in graph theory?

A set of vertices and edges

A set of nodes and arrows

A collection of matrices

A list of connected points

30. In graph theory, what does 'degree' of a vertex refer to?

The number of edges connected to a vertex

The number of vertices connected to an edge

The length of the shortest path to another vertex

The number of cycles passing through the vertex

Graph Theory MCQ Test 3