Graph Theory Ip

Lovely Professional University, PunjabCourse Code Course Title Course Planner Lectures Tutorials Practicals CreditsCSE223 GRAPH THEORY 14557::Avinash Kaur 3.0 0.0 0.0 3.0Course Category Courses with numerical and conceptual focus

TextBooks Sr No Title Author Edition Year Publisher NameT-1 Graph Theory J. A. Bondy and U. S. R.

Murty1st 2008 Springer

Reference BooksSr No Title Author Edition Year Publisher NameR-1 Graph Theory Russell Merris 1st 2013 Wiley Interscience, New York.R-2 D. B. West Introduction to Graph

Theory2nd 2004 PHI (Pretice Hall India)

R-3 Graph Theory V.K. Balakrishnan 1st 1997 Schaum Series McGraw Hill

Other Reading

Sr No Journals articles as Compulsary reading (specific articles, complete reference)OR-1 http://www.utm.edu/departments/math/graph/ ,

OR-2 http://cr.yp.to/2005-261/bender2/GT.pdf ,

OR-3 http://cs.bme.hu/fcs/graphtheory.pdf ,

OR-4 http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)1097-0118 , OR-5 http://www.personal.kent.edu/~rmuhamma/GraphTheory/graphTheory.htm ,

Relevant WebsitesSr No (Web address) (only if relevant to the course) Salient FeaturesRW-1 http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Euler_s_theorem.html Eulerian Theorem

RW-2 http://mathworld.wolfram.com/CompleteBipartiteGraph.html Bipartite Graph

RW-3 http://www3.ul.ie/cemtl/pdf%20files/cm2/CompleteGraph.pdf Complete Graph

RW-4 http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html Regular Graph

RW-5 http://vlsicad.eecs.umich.edu/BK/SAUCY/papers/Cameron2001.pdf Automorphism Groups

RW-6 http://cs.anu.edu.au/publications/eljc/Volume_17/PDF/v17i1r134.pdf Automorphism Groups and Reconstruction ProblemRW-7 http://www.math.smith.edu/~rhaas/papers/Trees.pdf Arboricity

RW-8 http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Euler_s_theorem.html Euler's Theorem

RW-9 http://www.cut-the-knot.org/do_you_know/CrossingNumber.shtml Crossing number and Thickness

RW-10 http://web.itu.edu.tr/~gencata/courses/GT/GTlecture10.pdf Decompostion and Domination

Audio Visual AidsSr No (AV aids) (only if relevant to the course) Salient FeaturesAV-1 http://freevideolectures.com/Course/3019/Graph-Theory Vertex Cover and Independent set

AV-2 http://www.nptel.iitm.ac.in/courses/106108054/ Various Topics of Graph Theory

AV-3 http://freevideolectures.com/Course/2768/MA-103-Topics-in-Contemporary-Mathematics/17

Temporary Mathematics

AV-4 http://www.cs.washington.edu/education/courses/cse421/06au/video/index.html Graph Theory

Software/Equipments/Databases

Sr No (S/E/D) (only if relevant to the course) Salient FeaturesSW-1 Prolog

Week Number

Lecture Number

Broad Topic(Sub Topic) Chapters/Sections of Text/reference books

Other Readings,Relevant Websites, Audio Visual Aids, software and Virtual Labs

Lecture Description Learning Outcomes Pedagogical ToolDemonstration/ Case Study / Images / animation / ppt etc. Planned

Week 1 Lecture 1 Basics(Graphs) T-1:Chapter 1 sec 1.1R-3:Chapter 1 sec

1.1 1.2

Introduction to the Graph Theory

Students comes to know about the basics of graph theory

Peer Learning , Discussion,Slides

Lecture 2 Basics(Graphs) T-1:Chapter 1 sec 1.1R-3:Chapter 1 sec

1.1 1.2

Introduction to the Graph Theory

Students comes to know about the basics of graph theory


Lecture 3 Basics(degree sequences) T-1:Chapter 1 sec 1.1 Basics of degree sequences

Understanding of the degree consequences


Week 2 Lecture 4 Basics(degree sequences) T-1:Chapter 1 sec 1.1 Basics of degree sequences

Understanding of the degree consequences


Detailed Plan For Lectures

LTP week distribution: (LTP Weeks)Weeks before MTE 7

Weeks After MTE 7

Spill Over 3

Week 2 Lecture 5 Basics(distance in graphs) R-3:Chapter 1 sec 1.1 1.2 1.3

Distance in Graphs Understanding of distance in graph


Lecture 6 Basics(distance in graphs) R-3:Chapter 1 sec 1.1 1.2 1.3

Distance in Graphs Understanding of distance in graph


Week 3 Lecture 7 Basics(complete graph) R-3:Chapter 1 RW-3 Introduction to complete graph

Students comes to know the complete graph


Lecture 8 Basics(complete graph) R-3:Chapter 1 RW-3 Introduction to complete graph

Students comes to know the complete graph


Lecture 9 Basics(regular and bipartite graphs)

R-3:Chapter 1 RW-2RW-4

Regular and Bipartite graph

To understanding two types regular and bipartite graphs


Week 4 Lecture 10 Basics(basic properties.) R-3:Chapter 1 Properties of Graphs Understanding of different properties of graphs


Lecture 11 Structure and Symmetry(Cut vertices)

T-1:Chapter 5 sec 5.1 Introduction to cut vertices

Students comes to know about the cut vertices


Lecture 12 Structure and Symmetry(Cut vertices)

T-1:Chapter 5 sec 5.1 Introduction to cut vertices

Students comes to know about the cut vertices


Week 5 Lecture 13 Structure and Symmetry(bridges and blocks)

T-1:Chapter 5 sec 5.2 Bridge and Block in the graphs, Lecture 13 considered as contingency lecture

Understanding the construction of the bridges and blocks in the graphs,Topic to be covered in lecture 12 and Test to be scheduled in lecture 13


Lecture 14 Quiz,Test 2Lecture 15 Structure and Symmetry

(automorphism groups)RW-5RW-6

Introduction to the automorphism groups

Basic understanding and use of automorphism groups


Week 6 Lecture 16 Structure and Symmetry(reconstruction problem.)

RW-6 Problem reconstruction Understanding of reconstruction problem in graphs


Lecture 17 Trees and connectivity(Properties of trees)

T-1:Chapter 4 sec 4.1 4.2 4.3 4.4

Different properties of trees

Understanding the properties and their use in graph


Lecture 18 Trees and connectivity(Properties of trees)

T-1:Chapter 4 sec 4.1 4.2 4.3 4.4

Different properties of trees

Understanding the properties and their use in graph


Week 7 Lecture 19 Trees and connectivity(Arboricity) RW-7 Introduction to arboricity student comes to know about the arboricity in the graphs theory


Week 7 Lecture 20 Trees and connectivity(vertex and edge connectivity)

T-1:Chapter 9 sec 9.1 9.2 9.3

Vertex and edge connectivity in graph theory

Understanding of the vertex and edge connectivity


Lecture 21 Trees and connectivity(Mengers theorem.)

T-1:Chapter 7 sec 7.3 Mengers theorem, Lecture 21 considered as contingency lecture

Mengers theorem explanation


MID-TERMWeek 8 Lecture 22 Eulerian and Hamiltonian graphs

(Characterization of Eulerian graphs)

T-1:Chapter 3 sec 3.1 Introduction and characterization of Eulerian graphs

Students will learn to about Eulerian graphs


Lecture 23 Eulerian and Hamiltonian graphs(Sufficient conditions for Hamiltonian graphs.)

T-1:Chapter 3 sec 3.2 Conditions for Hamiltonian graphs

Understanding the sufficient for hamiltonian graphs


Lecture 24 Colouring and planar graphs(Vertex and edge colouring)

T-1:Chapter 14 Chapter 17

Vertex and edge colouring to graphs

Understanding to color the edge and graphs


Week 9 Lecture 25 Colouring and planar graphs(Vertex and edge colouring)

T-1:Chapter 14 Chapter 17

Vertex and edge colouring to graphs

Understanding to color the edge and graphs


Colouring and planar graphs(perfect graphs)

T-1:Chapter 14 sec 14.4

Perfect graphs Student comes to know about the perfect graph


Lecture 26 Colouring and planar graphs(perfect graphs)


Perfect graphs Student comes to know about the perfect graph


Lecture 27 Colouring and planar graphs(planar graphs)

R-3:Chapter 8 sec 8.1 8.2

Planar graphs, Lecture 27 condsidered as contingency lecture

Student comes to know about the planar graphs,Topic to be covered in lecture 26 and Test to be scheduled in lecture 27


Week 10 Lecture 28 Quiz,Test 3Lecture 29 Colouring and planar graphs

(Euler's theorem)RW-1RW-8

Eulers Theorem Understanding of Euler s theorem


Lecture 30 Colouring and planar graphs(Kuratowski's theorem)

R-3:Chapter 8 sec 8.1

Kuratowskis Theorem Students comes to know about the kuratowskis theorem


Week 11 Lecture 31 Colouring and planar graphs(Kuratowski's theorem)


Kuratowskis Theorem Students comes to know about the kuratowskis theorem


Lecture 32 Colouring and planar graphs(Colouring of planar graphs)


Colouring of planar graphs

Understanding of planar graphs colouring


Lecture 33 Colouring and planar graphs(Colouring of planar graphs)


Colouring of planar graphs

Understanding of planar graphs colouring


Week 12 Lecture 34 Colouring and planar graphs(Crossing number and thickness.)

RW-9 Corssing number and thickness of graphs

Students comes to know about the crossing number and thickness


Lecture 35 Operations and Extremal Graph theory(Matching)


Matching Understanding of matching of graphs


Operations and Extremal Graph theory(factors)


Factors Understanding of factros


Operations and Extremal Graph theory(decomposition and domination)

RW-10 decomposition and domination,Topic to be covered in lecture 35 and Test to be scheduled in lecture 36

Understanding decomposition and domination,Topic to be covered in lecture 35 and Test to be scheduled in lecture 36


Lecture 36 Quiz,Test 1Week 13 Lecture 37 Operations and Extremal Graph

theory(Turan's theorem)T-1:Chapter 12 sec

12.1 12.2Turans theorem To be able to work on

Turans theoremPeer Learning , Discussion,Slides

Lecture 38 Operations and Extremal Graph theory(Ramsay's theorem)


Ramsays theorem To be able to work on Ramsays theorem


Lecture 39 Operations and Extremal Graph theory(Szemeredi's regularity lemma)


Szemeredis regularity lemma

To be able to work on Szemeredis regularity lemma


Week 14 Lecture 40 Operations and Extremal Graph theory(Szemeredi's regularity lemma)


Szemeredis regularity lemma

To be able to work on Szemeredis regularity lemma


Operations and Extremal Graph theory(applications.)


Application in graph theory

To be able to work on application in graph theory


Lecture 41 Operations and Extremal Graph theory(applications.)





Lecture 42 Operations and Extremal Graph theory(applications.)





SPILL OVERWeek 15 Lecture 43 Spill Over

Lecture 44 Spill Over

Lecture 45 Spill Over

Scheme for CA:

Component Frequency Out Of Each Marks Total Marks

Quiz,Test 2 3 10 20Total :- 10 20

Details of Academic Task(s)AT No. Objective Topic of the Academic Task Nature of Academic Task

(group/individuals/field work

Evaluation Mode Allottment / submission Week

Quiz 1 To engage the student in in depth knowledge of the course.

In a quiz (MCQ based Test) the questions must be so framed thatstudent is not able to answer through sheer guess work. Eachquestion must require some sought of analysis. The time limitshould be decided carefully according to the complexity ofquestions and number of questions per test. Typically themaximum time available for MCQ based test should be oneminute per question. Negative marking (25%) should be done toavoid guess work

Individual Performance in Quiz

12 / 12

Test 1 To test students knowledge and ability.

The test should consist of Analytical as well as descriptive questions.

Individual Based on performance in test

5 / 5

Test 2 To test students knowledge and ability.

The test should consist of analytical and descriptive questions Individual Based on performance in test

9 / 9

Graph Theory Ip

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