Explanation We have given a grid with a net pattern, we have to construct a graph that has a vertex corresponding to each net where two vertices are connected to one edge if and only if there can be a short circuit between the respective nets. Since, we know that the chromatic number of a graph G written as X ( G ) which is the minimum value of n for which an n -coloring of G exists. Also to divide a set of nets into subsets, if the two nets are in the same subset, there cannot be a smaller one between them. And, the minimum number of sub-sets obtainable in a suitable partition of the net is the qualitative number of the corresponding line-of-the-vis graph. So, the line-of-sight is before except for an additional edge between N 4 and N 7

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

3rd Edition

ISBN: 9780134689555

Author: Edgar Goodaire, Michael Parmenter

Publisher: PEARSON

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Chapter 13, Problem 17RE

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X(G) and find corresponding partition of the nets shown in right. Also draw the line-of sight graph associated with the net pattern.

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Chapter 13, Problem 16RE

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Use the Euclidean algorithm to find two sets of integers (a, b, c) such that 55a65b+143c: Solution = 1. By the Euclidean algorithm, we have: 143 = 2.65 + 13 and 65 = 5.13, so 13 = 143 – 2.65. - Also, 55 = 4.13+3, 13 = 4.3 + 1 and 3 = 3.1, so 1 = 13 — 4.3 = 13 — 4(55 – 4.13) = 17.13 – 4.55. Combining these, we have: 1 = 17(143 – 2.65) - 4.55 = −4.55 - 34.65 + 17.143, so we can take a = − −4, b = −34, c = 17. By carrying out the division algorithm in other ways, we obtain different solutions, such as 19.55 23.65 +7.143, so a = = 9, b -23, c = 7. = = how ? come [Note that 13.55 + 11.65 - 10.143 0, so we can obtain new solutions by adding multiples of this equation, or similar equations.]

Chapter 13 Solutions

Discrete Mathematics with Graph Theory (Classic Version) (3rd Edition) (Pearson Modern Classics for Advanced Mathematics Series)

Ch. 13.1 - Prob. 1TFQ Ch. 13.1 - Prob. 2TFQ Ch. 13.1 - Prob. 3TFQ Ch. 13.1 - Prob. 4TFQ Ch. 13.1 - Prob. 5TFQ Ch. 13.1 - Prob. 6TFQ Ch. 13.1 - Prob. 7TFQ Ch. 13.1 - Prob. 8TFQ Ch. 13.1 - Prob. 9TFQ Ch. 13.1 - Prob. 10TFQ

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X ( G ) and find corresponding partition of the nets shown in right. Also draw the line-of sight graph associated with the net pattern.

Solution Summary: The author explains how to draw the line-of-sight graph associated with the net pattern.

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X(G) and find corresponding partition of the nets shown in right. Also draw the line-of sight graph associated with the net pattern.

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Chapter 13 Solutions