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

1. 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

2. Which algorithm is used to find the shortest path in a weighted graph where some of the edge weights may be negative?

Dijkstra's Algorithm

Floyd-Warshall Algorithm

Bellman-Ford Algorithm

Kruskal's Algorithm

3. What is the term used for a graph that can be drawn in such a way that no edges cross each other?

Bipartite Graph

Planar Graph

Connected Graph

Cyclic Graph

4. In a bipartite graph, what does Hall's theorem state?

For every subset 'S' of the first vertex set, the neighborhood of 'S' is at least as large as 'S'.

For every subset 'S' of the second vertex set, the neighborhood of 'S' is at least as large as 'S'.

The maximum matching in the graph is equal to the minimum vertex cover.

The chromatic number is equal to the maximum degree.

5. 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

6. 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

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

Number of spanning trees

Chromatic number

Connectivity

Cycle detection

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

n-1

n/2

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

Euler's Theorem

Handshaking Lemma

Dijkstra's Theorem

Floyd-Warshall Theorem

10. 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

11. In a graph, what does a 'bridge' refer to?

A node with only one edge

An edge whose removal disconnects the graph

A complete subgraph

A node connected to all other nodes

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

Undirected Graph

Bipartite Graph

Directed Graph

Multigraph

13. What is the term used for a set of edges connecting two sets of vertices such that no two edges have a vertex in common?

Cut Set

Matching

Bridge Set

Independent Set

14. 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

15. In graph theory, what is the chromatic number of a cycle graph with 'n' vertices?

n/2

n-1

16. 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

17. 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

18. 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

19. In a graph, what does the term 'cut vertex' refer to?

An edge whose removal disconnects the graph

A vertex whose removal disconnects the graph

A vertex with only one edge

An edge that adds an extra connection

20. Which theorem states that in any graph, the number of vertices with odd degree is even?

Euler's Theorem

Handshaking Lemma

Pigeonhole Principle

Strong Connectivity Theorem

21. 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

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

n - 1

n^2

23. What is the minimum number of edges in a connected graph with 'n' vertices?

n - 1

n + 1

24. 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

25. Which graph theory problem involves finding a subset of vertices such that every edge in the graph has at least one of its endpoints in the subset?

Minimum Spanning Tree Problem

Cut Vertex Problem

Vertex Cover Problem

Hamiltonian Cycle Problem

26. Which of the following algorithms is used to find the minimum spanning tree of a graph?

Bellman-Ford Algorithm

Prim's Algorithm

Floyd-Warshall Algorithm

A* Search Algorithm

27. What does a Hamiltonian cycle in a graph refer to?

A cycle that visits every vertex exactly once

A cycle that ends where it started

A cycle with multiple endpoints

A cycle without any endpoints

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

n-1

n/2

29. 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

30. In a directed graph, what does the term 'strongly connected' mean?

There is a path from every vertex to every other vertex

There is a path from every vertex to at least one other vertex

Every vertex has a loop

There is a loop from every vertex to every other vertex

31. Which theorem states that in a connected graph, if every vertex has a degree of at least 'k', then the graph has a cycle of length at least 'k+1'?

Dirac's Theorem

Euler's Theorem

Konig's Theorem

Turan's Theorem

32. What is the edge connectivity of a complete graph with 'n' vertices?

n-1

n/2

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

34. Which graph theory problem deals with finding the smallest number of vertices that cover all the edges in a graph?

Vertex Cover Problem

Hamiltonian Path Problem

Eulerian Circuit Problem

Spanning Tree Problem

35. 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

36. In a weighted graph, what does the weight of an edge represent?

The distance between two vertices

The cost or value associated with traversing that edge

The number of paths using that edge

The number of vertices connected by that edge

37. In a weighted graph, what does the term 'cut' refer to?

A subset of edges that, when removed, disconnects the graph

A subset of vertices that, when removed, disconnects the graph

A vertex with a very high weight

An edge with a very low weight

38. 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

39. 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.

40. Which of the following is a graph where every edge is directed from one vertex to another?

Undirected Graph

Bipartite Graph

Directed Graph

Multigraph

Graph Theory MCQ Test 2