Discrete Mathematics | Representation of Graphs MCQs

Discrete Mathematics | Representation of Graphs MCQs: This section contains multiple-choice questions and answers on Representation of Graphs in Discrete Mathematics.
Submitted by Anushree Goswami, on July 27, 2022

1. Matrix representations of graphs G can be broken down into ___ main types?

  1. Two
  2. Three
  3. Four
  4. Five

Answer: A) Two

Explanation:

Matrix representations of graphs G can be broken down into two main types.


2. An _____ matrix are the two main ways to represent a graph G with a matrix?

  1. Adjacency
  2. Incidence
  3. Both A and B
  4. None of the above

Answer: C) Both A and B

Explanation:

An adjacency matrix and an incidence matrix are the two main ways to represent a graph G with a matrix.


3. aij = _ when a row and a column have an edge between vertex vi and vj?

  1. 0
  2. 1
  3. 2
  4. 3

Answer: B) 1

Explanation:

aij = 1 when a row and a column have an edge between vertex vi and vj.


4. When vertex vi and vj do not have edges, aij is equal to ___?

  1. Zero
  2. One
  3. Two
  4. Three

Answer: A) Zero

Explanation:

When vertex vi and vj do not have edges, aij is equal to Zero.


5. In the incident matrix, a ___ corresponds to each vertex and a ____ corresponds to each edge?

  1. Row, Column
  2. Column, Row
  3. Row, Row
  4. Column, Column

Answer: A) Row, Column

Explanation:

In the incident matrix, a row corresponds to each vertex and a column corresponds to each edge.


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6. Undirected graphs (without loops) have an incidence matrix equal to the ___?

  1. Degree multiplication of every vertex
  2. Degree sum of every vertex
  3. Degree multiplication of every edge
  4. Degree sum of every edge

Answer: B) Degree sum of every vertex

Explanation:

Undirected graphs (without loops) have an incidence matrix equal to the degree sum of every vertex.


7. Adjacency matrices of directed graphs contain the same number of ones as ___?

  1. Vertex
  2. Matrix
  3. Edge
  4. Label

Answer: C) Edge

Explanation:

Adjacency matrices of directed graphs contain the same number of ones as edges.


8. In the case where vertex vi and vertex vj have one or more edges, then aij=_, where _ = number of edges between vi and vj?

  1. 0
  2. 1
  3. 2
  4. N

Answer: D) N

Explanation:

In the case where vertex vi and vertex vj have one or more edges, then aij=N, where N = number of edges between vi and vj.



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