Explanation Definition used: Coloring of a graph: “The coloring for a graph is a method of coloring all vertices so that any pair of vertices joined by an edge has different colors.” Chromatic number: “The smallest number of color that required for a coloring of a graph is called as chromatic number of a graph.” Consider the states as the vertices and common borders as the edges. The graph representing the given map is shown in Figure 1. From the Figure 1 it can be observed that, there are nine vertices and sixteen edges. Color this graph by the following steps. Start at the vertex Cz with any color, namely green. The vertex Po is adjacent to the vertex Cz. So, color the vertex Po with different color, namely red. The vertex Be is adjacent to the vertices Po , but not adjacent to the vertex Cz . So, color the vertex Be with green color. The vertex Au is adjacent to the vertex Cz , but not adjacent to the vertex Po , so color the vertex Au with red...

3rd Edition

ISBN: 9781259969690

Author: sobecki

Publisher: MCG

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Chapter 13.1, Problem 50E

To determine

To find: The smallest number of colors needed to color the map so that no regions sharing a common border are the same color.

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Chapter 13.1, Problem 49E

Chapter 13.1, Problem 51E

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Chapter 13 Solutions

MATH IN OUR WORLD (LOOSELEAF)-W/ACCESS

Ch. 13.1 - Prob. 1TTO Ch. 13.1 - The floor plan shown in Figure 14-7 is for a...Ch. 13.1 - Prob. 3TTO Ch. 13.1 - Draw a graph for my neighborhood, shown in Figure...Ch. 13.1 - Prob. 5TTO Ch. 13.1 - Prob. 6TTO Ch. 13.1 - Prob. 7TTO Ch. 13.1 - Prob. 8TTO Ch. 13.1 - Prob. 1E Ch. 13.1 - What is the difference between a loop and a...

Ch. 13.1 - What is the difference between a circuit and a...Ch. 13.1 - Draw two graphs that look physically different but...Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 8E Ch. 13.1 - Prob. 9E Ch. 13.1 - Prob. 10E Ch. 13.1 - Prob. 11E Ch. 13.1 - How does graph coloring apply to maps?Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Prob. 18E Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Prob. 20E Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Use the following graph to answer Exercises 1324....Ch. 13.1 - Prob. 25E Ch. 13.1 - Prob. 26E Ch. 13.1 - 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The smallest number of colors needed to color the map so that no regions sharing a common border are the same color.

Solution Summary: The author explains that the smallest number of colors needed to color the map so that no regions sharing a common border are the same color is 4.

To find: The smallest number of colors needed to color the map so that no regions sharing a common border are the same color.

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Chapter 13 Solutions