Explanation Given information: The number of edges in the connected graph in the plane is 151. Formula used: The Euler characteristics theorem states that for connected graph in the plane the expression V − E + F is equal to 2. V − E + F = 2 ...... (1) Here, V is number of vertices, E is the number of edges, and F is the number of faces. Calculation: For the connected graph the Euler characteristic is 2. Substitute 151 for E in the equation (1) to obtain the relationship between the vertices and number of regions as, V − E + F

The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)

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ISBN: 9781119760054

Author: Burger, Edward B. , Starbird, Michael

Publisher: Wiley (WileyPLUS Products)

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Question

Chapter 6.2, Problem 14MS

To determine

To check: Whether the graph cuts the plane into 153 regions or not and also finds the largest number of region possible if it is not possible to have 153 regions.

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Chapter 6.2, Problem 13MS

Chapter 6.2, Problem 15MS

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Chapter 6 Solutions

The Heart of Mathematics: An Invitation to Effective Thinking, WileyPLUS NextGen Card with Loose-leaf Set Single Semester: An Invitation to Effective Thinking (Key Curriculum Press)

Ch. 6.1 - Map maker, map maker make me a graph. Represent...Ch. 6.1 - Unabridged list. Represent cach landmass from...Ch. 6.1 - Will the walk work? Does your graph from...Ch. 6.1 - Walk around the house. Is it possibel to traverse...Ch. 6.1 - Walk the line. Does this graph above have an Euler...Ch. 6.1 - Walkabout. Does this graph have an Euler circuit?...Ch. 6.1 - Linking the loops. In this map, the following...Ch. 6.1 - Scenic drive. (S) Here is a map of Rockystone...Ch. 6.1 - Under-edged. (H) Does this graph have an Euler...Ch. 6.1 - No man is an island. The country of Pelago...

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To check: Whether the graph cuts the plane into 153 regions or not and also finds the largest number of region possible if it is not possible to have 153 regions.

Solution Summary: The author explains that it is not possible to graph cuts the plane into 153 regions and the largest number of region possible is 152.

To check: Whether the graph cuts the plane into 153 regions or not and also finds the largest number of region possible if it is not possible to have 153 regions.

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Chapter 6 Solutions