graph theory final

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Graph Theory & it’s application

Presented by

Jit Saha

M.Tech CSE 1st year

03/05/12 jit saha-KGEC 1



Content

1. History of graph theory

2. Elementary concepts

3. Applications

4. Reference




1.History of graph theory

Leonhard Euler's paper on “Leonhard Euler's paper on “Seven BridgesSeven Bridges

of Königsberg”of Königsberg” ,,

published in 1736. published in 1736.


Content

walk about the city so ,crosseach bridge once & return to

the starting point.



1.History of graph theory-contd


Cycles in Polyhedra

Content



1.History of graph theory-contd


Four Colors of Maps

Content



2.Elementary concepts

• G(V,E) ,two sets of

objects

– Vertices (or nodes) ,set V

– Edges, set E

• Represented with circles

joined by lines

•

|V|=order of graph• | E |=size of graph


For the above simple

directed graph,

V ={A,B,C,D} E ={AB,BD,CD,AC,AD,BC}

|V |=4

| E|=6

Content



3.Applications

I. Computer Science

II. Chemistry

III. Operation Research

IV. Biological science

V. Other application


Content



I. Computer Science

• Data structure & Algorithm design

• Operating system

• DBMS

• Compiler design

• Computer networking & network security


Content

Application



Data structure & Algorithm design

• Serve as data structure

• Foundation of different algorithm

• Performance measurement

– Time complexity

– Space complexity


Content

Application



Operating system

• Modeling operating system

• Defining file structure

• Deadlock handling

• Defining storage structure

• Process scheduling


Content

Application



operating system-contd


Content

Application



DBMS

• Defining relation model

• ER diagram designing

• SQL Query optimization

• Transaction processing

– Precedence graph


Content Application



Compiler design

• Syntax tree construction

• Semantic checking

• Code optimization

– By DAG

• Graph coloring in

register optimization


Content

Application



Compiler design-contd

d=a+b

f=b/c

g=a+b

f=c+dd=f+c


DAG

representation

Graph coloring in

register allocation

Content

Applicatio



computer networking & network securuty

• Defining n/w topology

• path costs computation

– Routing protocols use

shortest path algorithms

• In multicast routing

protocol


Content

Application



computer networking & network securuty-

contd

• simulate propagation of

worms

– vertices are routing servers

–edges are the links

• Basec on minimum vertex

cover property

• finding the worm

propagation


vertex Set g={2,4,5}covers all the verticesin G

Content

Application



Other Computer Science application

• Search engine optimization

• Parallel algorithm solving

• software Engineering

• FSM model

• Computer architecture


content

application



II. Chemistry

• Structural representation of molecule

• Enumeration Chemical Isomers

• acyclic compounds are trees


Content

application



III. Operation research

• Solving LPP by

graphical method

• Estimating project

activity – PERT & CPM

• In Game Theory

– Using tree


content application



III. Operation research-contd


Game tree structurePert &CPM

content

application



IV. Biological Science

• statistical theory of

biological networks

• In DNA Sequencing


Example

-ATCGACTATAAGGC

ATCGAA

GAA

TCGCGA

GGC

GAC ACT

CTA

TAT ATA

AGGGGC

ATC

TAA

AAG

GCA

CAT

content

application



IV. Biological Science-contd

• Spread and Control of

Disease through Social

Networks – Social Network = Graph

– Vertices = People

– Edges = contact


content

application



V. Other application

• Utilities problem

• Electrical network problem

• Bus-trail network

• Pedigree(family tree)

• Telephone network systems


content

application



4. Reference

• Books

– Graph Theory with Applications to Engineering and

Computer Science by Narsingh Deo

–

Discrete Mathematics and Its Applications by Kenneth H.Rose

• URL

– http://en.wikipedia.org/wiki/Graph_theory

– http://mathworld.wolfram.com/GraphTheory.html

– http://www.britannica.com/EBchecked/topic/242012/graph-theor


http://en.wikipedia.org/wiki/Graph_theory

http://mathworld.wolfram.com/GraphTheory.html

http://www.britannica.com/EBchecked/topic/242012/graph-theory

http://www.britannica.com/EBchecked/topic/242012/graph-theory

http://mathworld.wolfram.com/GraphTheory.html

http://en.wikipedia.org/wiki/Graph_theory

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