Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
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
See similar textbooks
icon
Related questions
Question

Answer only question seven 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
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer