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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.

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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.

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3. a_ij = _ when a row and a column have an edge between vertex v_i and v_j?

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

Answer: B) 1

Explanation:

a_ij = 1 when a row and a column have an edge between vertex v_i and v_j.

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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.

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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.

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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.

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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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