Home »
MCQs »
Discrete Mathematics MCQs
Discrete Mathematics | Trees Introduction MCQs
Discrete Mathematics | Trees Introduction MCQs: This section contains multiple-choice questions and answers on Trees Introduction in Discrete Mathematics.
Submitted by Anushree Goswami, on October 23, 2022
1. Graphs without cycles are called ____ graphs?
- Cyclic
- Non-cyclic
- Acyclic
- None of the above
Answer: C) Acyclic
Explanation:
Graphs without cycles are called acyclic graphs.
2. Trees are ____?
- Acyclic graphs
- Graphs without cycles
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
Trees are acyclic graphs, or graphs without cycles.
3. The definition of a tree or general tree is a non-empty finite set of vertices or nodes with the property that each node can have a minimum degree of _, and a maximum degree of _?
- 1, N
- N, 1
- 1, Infinite
- N, Infinite
Answer: A) 1, N
Explanation:
The definition of a tree or general tree is a non-empty finite set of vertices or nodes with the property that each node can have a minimum degree of 1, and a maximum degree of N.
4. As long as the root of the tree is in the first subset and the remaining n subsets contain the elements of the n subtrees, then it can be partitioned into ___ disjoint subsets?
- n
- n+1
- n-1
- n--
Answer: B) n+1
Explanation:
As long as the root of the tree is in the first subset and the remaining n subsets contain the elements of the n subtrees, then it can be partitioned into n+1 disjoint subsets.
5. Directed trees are ____?
- Acyclic graphs
- Acyclic Undirected graphs
- Acyclic Directed graphs
- None of the above
Answer: C) Acyclic Directed graphs
Explanation:
Directed trees are acyclic directed graphs.
6. Directed trees call the nodes with outdegree 0 ____?
- External node
- Terminal node
- Leaf
- All of the above
Answer: D) All of the above
Explanation:
Directed trees call the nodes with outdegree 0 external nodes or terminal nodes, or leaves.
7. A node with an outdegree greater than or equal to one is considered an ____ node?
- Outer
- Internal
- External
- Terminal
Answer: B) Internal
Explanation:
A node with an outdegree greater than or equal to one is considered an internal node.
8. Whenever there is an ordering at each level of a tree, it is called an ____ tree?
- Ordered
- Unordered
- Disordered
- None
Answer: A) Ordered
Explanation:
Whenever there is an ordering at each level of a tree, it is called an ordered tree.
9. What is/are the property/ies of trees?
- Every pair of vertices in a tree has a single path between them.
- Trees are graphs whose vertices are connected to each other only by one path.
- There are n-1 edges in a tree T with n vertices.
- All of the above
Answer: D) All of the above
Explanation:
The properties of tress are-
- Every pair of vertices in a tree has a single path between them.
- Trees are graphs whose vertices are connected to each other only by one path.
- There are n-1 edges in a tree T with n vertices.
10. Trees that have one root node or vertex with incoming degrees of 0, and all other vertices with incoming degrees of 1, are called ____ trees?
- Internal
- Rooted
- Non-rooted
- External
Answer: B) Rooted
Explanation:
Trees that have one root node or vertex with incoming degrees of 0, and all other vertices with incoming degrees of 1, are called rooted trees.
11. Which of the following is a rooted tree?
- Tree with no nodes
- A single node with no children
- Both A and B
- None of the above
Answer: C) Both A and B
Explanation:
Following are the rooted trees -
- Tree with no nodes
- A single node with no children
12. Rooted tree with no nodes is also known as -?
- Full tree
- Empty tree
- Filled tree
- None of the above
Answer: B) Empty tree
Explanation:
Rooted tree with no nodes is also known as empty tree.
13. Rooted trees define vertex path length as the number of ____ that connect the root and the vertex?
- Vertex
- Edges
- Endpoints
- Cutpoints
Answer: B) Edges
Explanation:
Rooted trees define vertex path length as the number of edges that connect the root and the vertex.