Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Degree Sequence for Graph - Discrete Mathematics - Solved Homework, Slides of Discrete Mathematics

Shoolini University of Biotechnology and Management SciencesDiscrete Mathematics

During the study of discrete mathematics, I found this course very informative and applicable.The main points in these lecture slides are:Degree Sequence for Graph, Graph Bipartite, Subgraph of Graph, Induced by Vertices, Complimentary Graph, Pair of Nodes, Euler Theorem, Odd Degree, Repeated Edges, Sum of Degrees, Maximal Degree

Typology: Slides

2012/2013

Uploaded on 04/27/2013

atmaja
atmaja 🇮🇳

4.2

(45)

182 documents

1 / 3

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
CS173: Discrete Mathematical Structures
Spring 2006
Homework #13
Due 07/05/06, 8a
Solutions: 42 points, 3 points for each question.
1. You're given a graph:
a. Give a degree sequence for the graph.
Solution: 3,3,3,3,3,3,3,3.
b. Is the graph bipartite (answer without explanation will not be accepted).
Solution: Yes, blue and red points are the partition.
c. Draw the subgraph of this graph induced by the vertices {E,F,B,C,G}
d. Draw the complimentary graph.
Docsity.com
pf3

Partial preview of the text

Download Degree Sequence for Graph - Discrete Mathematics - Solved Homework and more Slides Discrete Mathematics in PDF only on Docsity!

CS173: Discrete Mathematical Structures Spring 2006 Homework # Due 07/05/06, 8a Solutions: 42 points, 3 points for each question.

  1. You're given a graph: a. Give a degree sequence for the graph. Solution: 3,3,3,3,3,3,3,3. b. Is the graph bipartite (answer without explanation will not be accepted). Solution: Yes, blue and red points are the partition. c. Draw the subgraph of this graph induced by the vertices {E,F,B,C,G} d. Draw the complimentary graph.

e. What is the largest complete subgraph that the graph contains? Solution: Any pair of nodes. The largest cliques size is 2. f. Can you traverse all the vertices starting from A visiting each vertex only once? Solution:Yes, for example: A,B,F,G,C,D,H,E,A g. Can you traverse all the edges visiting each edge exactly once? Solution: No, by Euler theorem at most 2 nodes can have an odd degree.

  1. Draw a graph with the given properties or prove why no such graph exists. a. Simple graph (no loops or repeated edges), six vertices each of degree 2 Solution: loop: 1->2->3->4->5->6->1. b. Simple graph having degree sequence 3,3,3, Solution: this is a complete graph. Just connect all possible vertices with edges. c. Graph with 6 edges and degree sequence 1,2,3,4, Solution: Sum of degrees is always twice the number of edges. This property doesn't hold here, thus the graph is impossible. d. Simple graph with six vertices and degree sequence 2,2,5,5,5, Solution: There are 4 vertices with degree 5, which means they're connected to all the other vertices in graph. Thus the minimal possible degree can be 4, not 2. Impossible e. A simple bipartite graph with 6 nodes and degree sequence 4,3,3,2,2, If an vertex in a bipartite graph has a degree 4, there are at least 4 nodes in the other part of the partition. Thus the bipartite graph must have two groups, one with 2 nodes and one with 4. Note that maximal degree allowed in a part with 4 nodes is 2 (both node on the other side). But one of the vertices with degrees 4,3,3 must be on the side of 4 nodes,