1. Which of the following is true about a directed graph?
A. It consists of only vertices.
B. Each edge is associated with a direction.
C. The edges have no weight or length.
D. It is a tree.
Answer: B) Each edge is associated with a direction.
Rationale: A directed graph (digraph) has edges that have specific directions, as
indicated by arrows, showing the flow from one vertex to another.
2. What is the degree of a vertex in a graph?
A. The number of edges connected to the vertex.
B. The sum of the weights of the edges connected to the vertex.
C. The number of vertices connected to the vertex.
D. The number of loops at the vertex.
Answer: A) The number of edges connected to the vertex.
Rationale: The degree of a vertex is simply the number of edges that are incident to it.
3. Which of the following is a property of a tree?
A. It contains cycles.
B. It is a connected graph with no cycles.
C. It has exactly one vertex.
D. It is a disconnected graph.
Answer: B) It is a connected graph with no cycles.
Rationale: A tree is a connected graph with no cycles and has exactly n−1n-1n−1
edges if it has nnn vertices.
4. In a graph, an edge with no direction is called a:
A. Loop.
B. Directed edge.
C. Undirected edge.
D. Path.
Answer: C) Undirected edge.
Rationale: An undirected edge has no direction and simply connects two vertices.
5. What does the term “connected graph” mean?
A. Every vertex is connected to every other vertex.
B. There is at least one path between any pair of vertices.
C. The graph has no edges.
D. The graph contains cycles.
Answer: B) There is at least one path between any pair of vertices.
Rationale: A connected graph ensures that for every pair of vertices, there is a path
that connects them, either directly or indirectly.
6. In a directed graph, if there is an edge from vertex A to vertex B, this is represented
by:
A. A bidirectional edge.
B. An arrow from A to B.
C. An undirected edge.
, D. A cycle.
Answer: B) An arrow from A to B.
Rationale: Directed edges in a graph are represented by arrows, indicating the direction
from one vertex to another.
7. What is the purpose of using Kruskal's Algorithm in decision mathematics?
A. To find the shortest path in a weighted graph.
B. To find the minimum spanning tree of a graph.
C. To find the shortest route between two nodes.
D. To find a Hamiltonian cycle in a graph.
Answer: B) To find the minimum spanning tree of a graph.
Rationale: Kruskal's algorithm is used to find the minimum spanning tree (MST) of a
graph by selecting edges with the smallest weights while avoiding cycles.
8. Which of the following is the characteristic of an Eulerian graph?
A. Every vertex has an even degree.
B. It contains exactly one Hamiltonian cycle.
C. It is a tree.
D. It is disconnected.
Answer: A) Every vertex has an even degree.
Rationale: An Eulerian graph has the property that every vertex has an even degree,
and it contains an Eulerian circuit (a closed path that visits every edge exactly once).
9. Which algorithm is used to find the shortest path in a graph with non-negative edge
weights?
A. Prim’s Algorithm.
B. Dijkstra’s Algorithm.
C. Kruskal’s Algorithm.
D. Bellman-Ford Algorithm.
Answer: B) Dijkstra’s Algorithm.
Rationale: Dijkstra’s algorithm finds the shortest path from a starting vertex to all other
vertices in a graph with non-negative edge weights.
10. Which of the following is NOT a valid operation on graphs?
A. Addition of an edge.
B. Deletion of a vertex.
C. Removal of a vertex's edges.
D. Change of the number of edges in a graph.
Answer: D) Change of the number of edges in a graph.
Rationale: The number of edges in a graph is determined by its structure, but the other
options involve operations on the graph that preserve or modify the structure without
fundamentally changing edge count.
11. Which of the following best describes a bipartite graph?
A. It contains no cycles.
B. It can be colored using two colors.
C. It has exactly one vertex.
D. It is a tree with two branches.
Answer: B) It can be colored using two colors.
Rationale: A bipartite graph is one where the vertex set can be divided into two disjoint
A. It consists of only vertices.
B. Each edge is associated with a direction.
C. The edges have no weight or length.
D. It is a tree.
Answer: B) Each edge is associated with a direction.
Rationale: A directed graph (digraph) has edges that have specific directions, as
indicated by arrows, showing the flow from one vertex to another.
2. What is the degree of a vertex in a graph?
A. The number of edges connected to the vertex.
B. The sum of the weights of the edges connected to the vertex.
C. The number of vertices connected to the vertex.
D. The number of loops at the vertex.
Answer: A) The number of edges connected to the vertex.
Rationale: The degree of a vertex is simply the number of edges that are incident to it.
3. Which of the following is a property of a tree?
A. It contains cycles.
B. It is a connected graph with no cycles.
C. It has exactly one vertex.
D. It is a disconnected graph.
Answer: B) It is a connected graph with no cycles.
Rationale: A tree is a connected graph with no cycles and has exactly n−1n-1n−1
edges if it has nnn vertices.
4. In a graph, an edge with no direction is called a:
A. Loop.
B. Directed edge.
C. Undirected edge.
D. Path.
Answer: C) Undirected edge.
Rationale: An undirected edge has no direction and simply connects two vertices.
5. What does the term “connected graph” mean?
A. Every vertex is connected to every other vertex.
B. There is at least one path between any pair of vertices.
C. The graph has no edges.
D. The graph contains cycles.
Answer: B) There is at least one path between any pair of vertices.
Rationale: A connected graph ensures that for every pair of vertices, there is a path
that connects them, either directly or indirectly.
6. In a directed graph, if there is an edge from vertex A to vertex B, this is represented
by:
A. A bidirectional edge.
B. An arrow from A to B.
C. An undirected edge.
, D. A cycle.
Answer: B) An arrow from A to B.
Rationale: Directed edges in a graph are represented by arrows, indicating the direction
from one vertex to another.
7. What is the purpose of using Kruskal's Algorithm in decision mathematics?
A. To find the shortest path in a weighted graph.
B. To find the minimum spanning tree of a graph.
C. To find the shortest route between two nodes.
D. To find a Hamiltonian cycle in a graph.
Answer: B) To find the minimum spanning tree of a graph.
Rationale: Kruskal's algorithm is used to find the minimum spanning tree (MST) of a
graph by selecting edges with the smallest weights while avoiding cycles.
8. Which of the following is the characteristic of an Eulerian graph?
A. Every vertex has an even degree.
B. It contains exactly one Hamiltonian cycle.
C. It is a tree.
D. It is disconnected.
Answer: A) Every vertex has an even degree.
Rationale: An Eulerian graph has the property that every vertex has an even degree,
and it contains an Eulerian circuit (a closed path that visits every edge exactly once).
9. Which algorithm is used to find the shortest path in a graph with non-negative edge
weights?
A. Prim’s Algorithm.
B. Dijkstra’s Algorithm.
C. Kruskal’s Algorithm.
D. Bellman-Ford Algorithm.
Answer: B) Dijkstra’s Algorithm.
Rationale: Dijkstra’s algorithm finds the shortest path from a starting vertex to all other
vertices in a graph with non-negative edge weights.
10. Which of the following is NOT a valid operation on graphs?
A. Addition of an edge.
B. Deletion of a vertex.
C. Removal of a vertex's edges.
D. Change of the number of edges in a graph.
Answer: D) Change of the number of edges in a graph.
Rationale: The number of edges in a graph is determined by its structure, but the other
options involve operations on the graph that preserve or modify the structure without
fundamentally changing edge count.
11. Which of the following best describes a bipartite graph?
A. It contains no cycles.
B. It can be colored using two colors.
C. It has exactly one vertex.
D. It is a tree with two branches.
Answer: B) It can be colored using two colors.
Rationale: A bipartite graph is one where the vertex set can be divided into two disjoint
