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7. 8. 9. 10. Let G be a regular graph with at least one edge. Assume that there is a way of partitioning the set of vertices of G into two sets X, Y such that this partition makes G bipartite. Prove that |X| = |Y. Let G be a regular graph with a vertex of degree 4 and 10 edges. How many vertices does it have? Prove that the complement of a regular graph is also regular. Prove that a bipartite graph on n vertices has a number of edges less or equal to 2

7. 8. 9. 10. Let G be a regular graph with at least one edge. Assume that there is a way of partitioning the set of vertices of G into two sets X, Y such that this partition makes G bipartite. Prove that |X| = |Y. Let G be a regular graph with a vertex of degree 4 and 10 edges. How many vertices does it have? Prove that the complement of a regular graph is also regular. Prove that a bipartite graph on n vertices has a number of edges less or equal to 2

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter3: Matrices
Section3.7: Applications
Problem 80EQ
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Answer only question nine and it's a applied discrete mathematics question 

7. 8. 9. 10. Let G be a regular graph with at least one edge. Assume that there is a way of partitioning the set of vertices of G into two sets X, Y such that this partition makes G bipartite. Prove that |X| = |Y. Let G be a regular graph with a vertex of degree 4 and 10 edges. How many vertices does it have? Prove that the complement of a regular graph is also regular. Prove that a bipartite graph on n vertices has a number of edges less or equal to 2
Transcribed Image Text:7. 8. 9. 10. Let G be a regular graph with at least one edge. Assume that there is a way of partitioning the set of vertices of G into two sets X, Y such that this partition makes G bipartite. Prove that |X| = |Y. Let G be a regular graph with a vertex of degree 4 and 10 edges. How many vertices does it have? Prove that the complement of a regular graph is also regular. Prove that a bipartite graph on n vertices has a number of edges less or equal to 2
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