1. Which of the following algorithms is used to find the maximum flow in a network?
A. Ford-Fulkerson Algorithm.
B. Dijkstra’s Algorithm.
C. Kruskal’s Algorithm.
D. Bellman-Ford Algorithm.
Answer: A) Ford-Fulkerson Algorithm.
Rationale: The Ford-Fulkerson algorithm is used to find the maximum flow in a flow
network by augmenting paths from the source to the sink.
2. 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.
3. Which algorithm is used to solve the all-pairs shortest path problem in a graph?
A. Bellman-Ford Algorithm.
B. Dijkstra’s Algorithm.
C. Floyd-Warshall Algorithm.
D. Prim’s Algorithm.
Answer: C) Floyd-Warshall Algorithm.
Rationale: The Floyd-Warshall algorithm is designed to find the shortest paths between
all pairs of vertices in a graph.
4. In the context of decision mathematics, what is a network flow problem?
A. Finding the shortest path between two vertices.
B. Assigning workers to tasks.
C. Determining the maximum amount of flow that can pass through a network of nodes
and edges.
D. Coloring the vertices of a graph.
Answer: C) Determining the maximum amount of flow that can pass through a network
of nodes and edges.
Rationale: Network flow problems involve finding the maximum flow in a network from
a source to a sink.
5. What is the degree of vertex A in the graph shown below (considering undirected
edges)?
(Graph with edges: A-B, A-C, A-D, B-C, D-E)
A. 1
B. 2
C. 3
D. 4
Answer: D) 4
Rationale: Vertex A is connected by edges to vertices B, C, and D, which gives it a
, degree of 4.
6. In an undirected graph, a loop is:
A. An edge that connects a vertex to itself.
B. An edge connecting two different vertices.
C. A cycle that includes multiple vertices.
D. A directed edge.
Answer: A) An edge that connects a vertex to itself.
Rationale: A loop in an undirected graph is an edge that connects a vertex to itself.
7. What is the time complexity of Dijkstra’s Algorithm using an adjacency matrix?
A. O(V2)O(V^2)O(V2)
B. O(VlogV)O(V \log V)O(VlogV)
C. O(E+V)O(E + V)O(E+V)
D. O(V3)O(V^3)O(V3)
Answer: A) O(V2)O(V^2)O(V2)
Rationale: Using an adjacency matrix, the time complexity of Dijkstra’s algorithm is
O(V2)O(V^2)O(V2) because the algorithm needs to scan through the entire matrix for
each vertex.
8. 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
sets such that every edge connects a vertex from one set to a vertex from the other
set.
9. Which of the following is a necessary condition for an undirected graph to have an
Eulerian circuit?
A. All vertices have even degree.
B. The graph is bipartite.
C. The graph is connected.
D. All vertices have odd degree.
Answer: A) All vertices have even degree.
Rationale: For an undirected graph to have an Eulerian circuit, all vertices must have
even degrees, and the graph must be connected.
10. Which of the following is a characteristic of a Hamiltonian cycle?
A. It visits every edge exactly once.
B. It visits every vertex exactly once and returns to the starting vertex.
C. It visits every vertex multiple times.
D. It is not connected.
Answer: B) It visits every vertex exactly once and returns to the starting vertex.
Rationale: A Hamiltonian cycle visits every vertex exactly once and forms a closed loop
by returning to the starting vertex.
11. In a bipartite graph, how can the vertex set be divided?
A. Ford-Fulkerson Algorithm.
B. Dijkstra’s Algorithm.
C. Kruskal’s Algorithm.
D. Bellman-Ford Algorithm.
Answer: A) Ford-Fulkerson Algorithm.
Rationale: The Ford-Fulkerson algorithm is used to find the maximum flow in a flow
network by augmenting paths from the source to the sink.
2. 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.
3. Which algorithm is used to solve the all-pairs shortest path problem in a graph?
A. Bellman-Ford Algorithm.
B. Dijkstra’s Algorithm.
C. Floyd-Warshall Algorithm.
D. Prim’s Algorithm.
Answer: C) Floyd-Warshall Algorithm.
Rationale: The Floyd-Warshall algorithm is designed to find the shortest paths between
all pairs of vertices in a graph.
4. In the context of decision mathematics, what is a network flow problem?
A. Finding the shortest path between two vertices.
B. Assigning workers to tasks.
C. Determining the maximum amount of flow that can pass through a network of nodes
and edges.
D. Coloring the vertices of a graph.
Answer: C) Determining the maximum amount of flow that can pass through a network
of nodes and edges.
Rationale: Network flow problems involve finding the maximum flow in a network from
a source to a sink.
5. What is the degree of vertex A in the graph shown below (considering undirected
edges)?
(Graph with edges: A-B, A-C, A-D, B-C, D-E)
A. 1
B. 2
C. 3
D. 4
Answer: D) 4
Rationale: Vertex A is connected by edges to vertices B, C, and D, which gives it a
, degree of 4.
6. In an undirected graph, a loop is:
A. An edge that connects a vertex to itself.
B. An edge connecting two different vertices.
C. A cycle that includes multiple vertices.
D. A directed edge.
Answer: A) An edge that connects a vertex to itself.
Rationale: A loop in an undirected graph is an edge that connects a vertex to itself.
7. What is the time complexity of Dijkstra’s Algorithm using an adjacency matrix?
A. O(V2)O(V^2)O(V2)
B. O(VlogV)O(V \log V)O(VlogV)
C. O(E+V)O(E + V)O(E+V)
D. O(V3)O(V^3)O(V3)
Answer: A) O(V2)O(V^2)O(V2)
Rationale: Using an adjacency matrix, the time complexity of Dijkstra’s algorithm is
O(V2)O(V^2)O(V2) because the algorithm needs to scan through the entire matrix for
each vertex.
8. 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
sets such that every edge connects a vertex from one set to a vertex from the other
set.
9. Which of the following is a necessary condition for an undirected graph to have an
Eulerian circuit?
A. All vertices have even degree.
B. The graph is bipartite.
C. The graph is connected.
D. All vertices have odd degree.
Answer: A) All vertices have even degree.
Rationale: For an undirected graph to have an Eulerian circuit, all vertices must have
even degrees, and the graph must be connected.
10. Which of the following is a characteristic of a Hamiltonian cycle?
A. It visits every edge exactly once.
B. It visits every vertex exactly once and returns to the starting vertex.
C. It visits every vertex multiple times.
D. It is not connected.
Answer: B) It visits every vertex exactly once and returns to the starting vertex.
Rationale: A Hamiltonian cycle visits every vertex exactly once and forms a closed loop
by returning to the starting vertex.
11. In a bipartite graph, how can the vertex set be divided?
