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Consider a bipartite graph on the set A = {1,2,3,4,5,6} and B = {7,8,9,10,11,12}, where there is an edge between xe A and y e B if and only if x+y is a multiple of 4. What is the size of N({2})? What is the size of N({2,5})? What is the size of N({2,6})? Is there a matching in this graph?

Consider a bipartite graph on the set A = {1,2,3,4,5,6} and B = {7,8,9,10,11,12}, where there is an edge between xe A and y e B if and only if x+y is a multiple of 4. What is the size of N({2})? What is the size of N({2,5})? What is the size of N({2,6})? Is there a matching in this graph?

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter1: Line And Angle Relationships
Section1.5: The Format Proof Of A Theorem
Problem 12E: Based upon the hypothesis of a theorem, do the drawings of different students have to be identical...
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WHat would be the size of N{ 2 }

Size of N { 2,5 }

Size of N { 2,6}

 

are there any matches here? 

 

Consider a bipartite graph on the set A = {1,2,3,4,5,6} and B = {7,8,9,10,11,12}, where there is an edge between xe A and y e B if and only if x+y is a multiple of 4. What is the size of N({2})? What is the size of N({2,5})? What is the size of N({2,6})? Is there a matching in this graph?
Transcribed Image Text:Consider a bipartite graph on the set A = {1,2,3,4,5,6} and B = {7,8,9,10,11,12}, where there is an edge between xe A and y e B if and only if x+y is a multiple of 4. What is the size of N({2})? What is the size of N({2,5})? What is the size of N({2,6})? Is there a matching in this graph?
Expert Solution
Step 1

Given:

A bipartite graph is defined on set A={1,2,3,4,5,6} and   

B={7,8,9,10,11,12}.

Here there is an edge between x∈A and x∈B if and only if x+y is multiple of 4.

The edges will be between the set of points (x, y):

 (1, 7), (1, 11), (2, 10), (3, 9), (4, 8), (4, 12), (5, 7), (5, 11), (6, 10)

Drawing the graph we get,

Advanced Math homework question answer, step 1, image 1

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