{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# hw8 - O 2(b[3 marks Draw a graph with the same number of...

This preview shows page 1. Sign up to view the full content.

ECE 103 Discrete Math for Engineers University of Waterloo Spring 2010 Instructors: Koray Karabina, Ashwin Nayak Homework 8, due July 19, 2010 The first four questions pertain to the following class of graph. The odd graph O n is the graph whose vertices are the n -subsets of { 1 , 2 ,..., 2 n, 2 n + 1 } . Two such sets are adjacent (i.e., form an edge) if and only if they are disjoint. Question 1. (a) [2 marks] Draw O 1 , and O 2 . In the drawing for O 2 , draw the vertices, but only the edges incident on vertices { 1 , 2 } , { 2 , 4 } and { 4 , 5 } . (b) [3 marks] How many vertices and edges does O n have? Question 2. [5 marks] Prove that there is no cycle of length 3 or 4 in O 2 . Question 3. (a) [2 marks] Describe an isomorphism between O 2 and the Peterson graph drawn below, by labelling the vertices of the Peterson graph by vertices of
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: O 2 . (b) [3 marks] Draw a graph with the same number of vertices and edges as in O 2 , and in which the degree of every vertex is 3, that is not isomorphic to O 2 . Explain why it is not isomorphic. Question 4. (a) [2 marks] Describe a path in the graph O n between the vertices { 1 , 2 , . . . , n-1 , n } and { 1 , 2 , 3 , . . . , n-1 , n + 1 } . (b) [3 marks] Use the idea in part (a) to show that there is a path from the vertex { 1 , 2 , . . . , n-1 , n } to the vertex { 1 , 2 , 3 , . . . , n-2 , n + 1 , n + 2 } in the graph O n . Question 5. [5 marks] Describe a cycle in the grid graph G n , for any even n that contains all the n 2 vertices. Prove that no cycle in G 3 contains all its vertices. 1...
View Full Document

{[ snackBarMessage ]}