sample1 soln

# sample1 soln - AMS 301 Sample Exam 1 Solution Ning SUN July...

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: AMS 301 Sample Exam 1 Solution Ning SUN July 27, 2009 1 True or False. 1. True. Let k be the degree of all vertices in G , and let n be the number of vertices. The degree of vertex i in G plus the degree of vertex i in ¯ G is equal to n- 1 , the degree in a complete graph K n . Thus, each vertex of the complement graph must have degree n- 1- k . 2. True. There cannot exist K 5 or K 3 , 3 con gurations since the graph has only 2 vertices of degree n and all other vertices have degree 2. This can also be seen by giving a planar depiction. 1. True. By Euler's Theorem, if the graph is connected and every vertex has even degree (4 is even), then an Euler cycle exists. 2 Isomorphic? The graphs are NOT isomorphic. • The graphs have the same number of vertices, 8, and all have degree 3. • The left one is bipartite (see the following bipartite depiction), but the right one is not, as it has several odd circuits, such as 1-2-3-4-5-1....
View Full Document

## This note was uploaded on 11/29/2011 for the course AMS 301 taught by Professor Arkin during the Spring '08 term at SUNY Stony Brook.

### Page1 / 3

sample1 soln - AMS 301 Sample Exam 1 Solution Ning SUN July...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online