graph theory final

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Graph Theory & it’s application

Presented by

Jit Saha

M.Tech CSE 1st year

3/14/2012 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 “Seven Bridges

of Königsberg” ,

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

Application



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} coversall the vertices in 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

AGGGC

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-

theory


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

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

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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