# Discete Math

1) Let G be the graph whose vertices are all permutations of the integers of the set {1,2,…,10} with the property that two vertices (ε1,ε2,…,ε10) , (ε′1,ε′2, ...,ε′10) are connected by an edge if one vertex arises from the other by exchanging the positions of two integers εi,εj with εi,εj≤5

For example the vertices (1,**2**,7,4,8,**5**,3,10,9,6), (1,**5**,7,4,8,**2**,3,10,9,6) form an edge, vertices (1,**2**,4,8,**10**,7,3,5,9,6), (1,**10**,4,8,**2**,7,3,5,9,6) do not form an edge, vertices (1,**7**,2,4,8,**10**,3,5,9,6) , (1,**10**,2,4,8,**7**,3,5,9,6) do not form an edge. Find the number of edges of the graph G

2)How many induced subgraphs with 4 vertices does the complete graph K10 have? (We consider the vertices of K10 distinguished, i.e. named from 1 to 10)

3) The graph in the figure below is bipartite. Right or wrong?

## Answer

**Answers can be viewed only if**

- The questioner was satisfied and accepted the answer, or
- The answer was disputed, but the judge evaluated it as 100% correct.

1 Attachment

- answered
- 227 views
- $20.00

### Related Questions

- Combinatorics/counting: How many configurations are possible for m differenct objects in n boxes of unlimited occupany (m<n)
- Logic Questions (𝐴→𝐶)∧(𝐵→𝐶)⊢(𝐴∧𝐵)→𝐶
- Count the number of decks of cards, where no king is on top of the ace of the same suit.
- Markov Process Problem
- [Discrete Mathematics] For {1,3,6,10,15,…}. Find a recursive formula.
- Discrete math
- Discrete Structures - Proving a statement true
- Let A be an uncountable set, B a countable subset of A, and C the complement of B in A. Prove that there exists a one-to-one correspondence between A and C.

Low bounty.

just increased it