What is the chromatic number of the given graph? b d
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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![**Question:**
What is the chromatic number of the given graph?
**Graph Description:**
The graph consists of seven vertices labeled as a, b, c, d, e, f, and g. The connections between the vertices are as follows:
- Vertex a is connected to vertices b, f, and g.
- Vertex b is connected to vertices a, c, and g.
- Vertex c is connected to vertices b, d, and g.
- Vertex d is connected to vertices c, e, and g.
- Vertex e is connected to vertices d and f.
- Vertex f is connected to vertices a and e.
- Vertex g is connected to all surrounding vertices (a, b, c, d).
This structure forms two triangles (a, b, g) and (c, d, g) with a quadrilateral (a, f, e, d) connected through g.
**Chromatic Number:**
The chromatic number is the smallest number of colors needed to color the vertices so that no two adjacent vertices share the same color.
*[Provide your answer in the box below]*
[ ]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faeace8dd-c81d-480f-acf2-febf16f28112%2F5f4ebd33-8fc0-451f-b15a-d693d289d0ee%2Fqf8mtjq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
What is the chromatic number of the given graph?
**Graph Description:**
The graph consists of seven vertices labeled as a, b, c, d, e, f, and g. The connections between the vertices are as follows:
- Vertex a is connected to vertices b, f, and g.
- Vertex b is connected to vertices a, c, and g.
- Vertex c is connected to vertices b, d, and g.
- Vertex d is connected to vertices c, e, and g.
- Vertex e is connected to vertices d and f.
- Vertex f is connected to vertices a and e.
- Vertex g is connected to all surrounding vertices (a, b, c, d).
This structure forms two triangles (a, b, g) and (c, d, g) with a quadrilateral (a, f, e, d) connected through g.
**Chromatic Number:**
The chromatic number is the smallest number of colors needed to color the vertices so that no two adjacent vertices share the same color.
*[Provide your answer in the box below]*
[ ]
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