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Draw the graph represented by the following adjacency matrix. a b c d e f EDC F a b с d e f 0 0 1 0 0 1 0 2 0 1 20 1 0 0 0 0 1 0 1 0 0 1 0 0 2 0 1 00 1 0 1 0 0 0

Draw the graph represented by the following adjacency matrix. a b c d e f EDC F a b с d e f 0 0 1 0 0 1 0 2 0 1 20 1 0 0 0 0 1 0 1 0 0 1 0 0 2 0 1 00 1 0 1 0 0 0

Advanced Engineering Mathematics
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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**Title: Understanding Graph Representation through Adjacency Matrix** **Introduction:** This section will explain how to draw a graph using a given adjacency matrix. An adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. **Adjacency Matrix:** The given adjacency matrix is as follows: ``` a b c d e f a [ 0 0 1 0 0 1 ] b [ 0 2 0 1 2 0 ] c [ 1 0 0 0 0 1 ] d [ 0 1 0 0 1 0 ] e [ 0 2 0 1 0 0 ] f [ 1 0 1 0 0 0 ] ``` **Explanation:** - **Vertices**: The graph has 6 vertices labeled as a, b, c, d, e, and f. - **Matrix Entries**: The entries in the matrix represent the number of edges between the corresponding vertices. - A '0' indicates no edge between vertices. - A '1' indicates a single edge between vertices. - Higher numbers, such as '2', indicate multiple edges between the same vertices (parallel edges). **Graph Representation:** - Vertex 'a' is connected to vertices 'c' and 'f'. - Vertex 'b' has two loops (self-connections) and is connected to vertices 'd' and 'e' with one and two edges, respectively. - Vertex 'c' is connected to 'a' and 'f'. - Vertex 'd' is connected to 'b' and 'e'. - Vertex 'e' is connected to vertices 'b' and 'd'. - Vertex 'f' is connected to vertices 'a' and 'c'. **Conclusion:** By interpreting the adjacency matrix, we can successfully construct the graph, identifying the presence and number of edges between various vertices. This is essential for understanding the structure and properties of the graph being studied.
Transcribed Image Text:**Title: Understanding Graph Representation through Adjacency Matrix** **Introduction:** This section will explain how to draw a graph using a given adjacency matrix. An adjacency matrix is a square matrix used to represent a finite graph. The elements of the matrix indicate whether pairs of vertices are adjacent or not in the graph. **Adjacency Matrix:** The given adjacency matrix is as follows: ``` a b c d e f a [ 0 0 1 0 0 1 ] b [ 0 2 0 1 2 0 ] c [ 1 0 0 0 0 1 ] d [ 0 1 0 0 1 0 ] e [ 0 2 0 1 0 0 ] f [ 1 0 1 0 0 0 ] ``` **Explanation:** - **Vertices**: The graph has 6 vertices labeled as a, b, c, d, e, and f. - **Matrix Entries**: The entries in the matrix represent the number of edges between the corresponding vertices. - A '0' indicates no edge between vertices. - A '1' indicates a single edge between vertices. - Higher numbers, such as '2', indicate multiple edges between the same vertices (parallel edges). **Graph Representation:** - Vertex 'a' is connected to vertices 'c' and 'f'. - Vertex 'b' has two loops (self-connections) and is connected to vertices 'd' and 'e' with one and two edges, respectively. - Vertex 'c' is connected to 'a' and 'f'. - Vertex 'd' is connected to 'b' and 'e'. - Vertex 'e' is connected to vertices 'b' and 'd'. - Vertex 'f' is connected to vertices 'a' and 'c'. **Conclusion:** By interpreting the adjacency matrix, we can successfully construct the graph, identifying the presence and number of edges between various vertices. This is essential for understanding the structure and properties of the graph being studied.
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