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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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**Graph Coloring Using Greedy Algorithm** *Problem Statement:* Consider the following graph. Show the coloring produced by the greedy algorithm when the vertices are colored in the specified order. *Graph Description:* - The graph consists of six vertices labeled: a, b, c, d, e, and f. - The edges connect the vertices in the following manner: - Vertex a is connected to vertices b and f. - Vertex b is connected to vertices a, c, and d. - Vertex c is connected to vertices b and d. - Vertex d is connected to vertices b, c, and e. - Vertex e is connected to vertex d. - Vertex f is connected to vertex a and e. *Order of Vertex Coloring:* 1. b 2. d 3. e 4. a 5. c 6. f *Order of Colors:* 1. Red 2. Blue 3. Green 4. Yellow *Instructions for Coloring:* Apply the greedy algorithm to color the vertices in the given order, using the least number of colors without two adjacent vertices sharing the same color. Start with the first available color from the list for every vertex, following the specified order of vertices.
Transcribed Image Text:**Graph Coloring Using Greedy Algorithm** *Problem Statement:* Consider the following graph. Show the coloring produced by the greedy algorithm when the vertices are colored in the specified order. *Graph Description:* - The graph consists of six vertices labeled: a, b, c, d, e, and f. - The edges connect the vertices in the following manner: - Vertex a is connected to vertices b and f. - Vertex b is connected to vertices a, c, and d. - Vertex c is connected to vertices b and d. - Vertex d is connected to vertices b, c, and e. - Vertex e is connected to vertex d. - Vertex f is connected to vertex a and e. *Order of Vertex Coloring:* 1. b 2. d 3. e 4. a 5. c 6. f *Order of Colors:* 1. Red 2. Blue 3. Green 4. Yellow *Instructions for Coloring:* Apply the greedy algorithm to color the vertices in the given order, using the least number of colors without two adjacent vertices sharing the same color. Start with the first available color from the list for every vertex, following the specified order of vertices.
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