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For each of the following graphs, find the chromatic number and provide a coloring that demonstrates it is possible. In your drawing, make sure the graphs are large enough so that it is clear what the colors are! (a) (b) (c) *

For each of the following graphs, find the chromatic number and provide a coloring that demonstrates it is possible. In your drawing, make sure the graphs are large enough so that it is clear what the colors are! (a) (b) (c) *

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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**Problem 1: Chromatic Number of Graphs** For each of the following graphs, find the chromatic number and provide a coloring that demonstrates it is possible. In your drawing, make sure the graphs are large enough so that it is clear what the colors are! **Graph (a):** - Description: A complete graph on five vertices (K5), where each vertex is connected to every other vertex. The diagram forms a pentagon with intersecting diagonals inside. **Graph (b):** - Description: A graph with a pentagonal outer circuit and a star-like inner structure. Each vertex of the pentagon is connected to a central vertex, forming a set of triangles within the pentagon. **Graph (c):** - Description: A star graph with eight leaves. A central vertex is connected to eight outer vertices, each through individual edges, resembling a star or a wheel with spokes. **Task:** Determine the chromatic number for each graph and illustrate the coloring scheme clearly.
Transcribed Image Text:**Problem 1: Chromatic Number of Graphs** For each of the following graphs, find the chromatic number and provide a coloring that demonstrates it is possible. In your drawing, make sure the graphs are large enough so that it is clear what the colors are! **Graph (a):** - Description: A complete graph on five vertices (K5), where each vertex is connected to every other vertex. The diagram forms a pentagon with intersecting diagonals inside. **Graph (b):** - Description: A graph with a pentagonal outer circuit and a star-like inner structure. Each vertex of the pentagon is connected to a central vertex, forming a set of triangles within the pentagon. **Graph (c):** - Description: A star graph with eight leaves. A central vertex is connected to eight outer vertices, each through individual edges, resembling a star or a wheel with spokes. **Task:** Determine the chromatic number for each graph and illustrate the coloring scheme clearly.
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