Indicate if each of the two graphs are equal
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Indicate if each of the two graphs are equal
![The image consists of a graph diagram on the left and a matrix representation on the right.
**Graph Diagram:**
- It is a simple undirected graph with five vertices labeled as a, b, c, d, and e.
- The edges between these vertices are as follows:
- a is connected to b and e.
- b is connected to a, c, and d.
- c is connected to b and e.
- d is connected to b and e.
- e is connected to a, c, and d.
**Adjacency Matrix:**
The matrix representation of the graph is a 5x5 matrix, where the rows and columns correspond to vertices a, b, c, d, and e in that order. The entries in the matrix are either 0 or 1, indicating the absence or presence of an edge between the vertices.
\[
\begin{pmatrix}
0 & 1 & 0 & 0 & 1 \\
1 & 0 & 1 & 1 & 0 \\
0 & 1 & 0 & 0 & 1 \\
0 & 1 & 0 & 0 & 1 \\
1 & 0 & 1 & 1 & 0
\end{pmatrix}
\]
- The diagonal entries are all 0, indicating there are no self-loops.
- The matrix is symmetric, reflecting the undirected nature of the graph.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9f2920b9-16cb-409a-b0d9-184574689b7b%2F8053ced3-c338-4452-9b65-75f690f45bee%2Fo1wci1d_processed.png&w=3840&q=75)
Transcribed Image Text:The image consists of a graph diagram on the left and a matrix representation on the right.
**Graph Diagram:**
- It is a simple undirected graph with five vertices labeled as a, b, c, d, and e.
- The edges between these vertices are as follows:
- a is connected to b and e.
- b is connected to a, c, and d.
- c is connected to b and e.
- d is connected to b and e.
- e is connected to a, c, and d.
**Adjacency Matrix:**
The matrix representation of the graph is a 5x5 matrix, where the rows and columns correspond to vertices a, b, c, d, and e in that order. The entries in the matrix are either 0 or 1, indicating the absence or presence of an edge between the vertices.
\[
\begin{pmatrix}
0 & 1 & 0 & 0 & 1 \\
1 & 0 & 1 & 1 & 0 \\
0 & 1 & 0 & 0 & 1 \\
0 & 1 & 0 & 0 & 1 \\
1 & 0 & 1 & 1 & 0
\end{pmatrix}
\]
- The diagonal entries are all 0, indicating there are no self-loops.
- The matrix is symmetric, reflecting the undirected nature of the graph.
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