The document discusses several real-life applications of network graph theory, including: 1) Modeling GSM mobile phone networks as graphs, where each cell is represented as a node and cells that border each other are connected by edges. This allows analyzing network coverage and optimization. 2) Using graph coloring to assign frequencies to cells in a GSM network so that neighboring cells do not use the same frequency and cause interference. Only four colors are needed, relating to the Four Color Theorem. 3) Analyzing transportation and routing problems as graphs, such as modeling streets in a city as a graph to determine if one-way streets can be implemented without disconnecting areas.

1. REAL LIFE APPLICATIONS OF
NETWORK GRAPH THEORY
BY
G.NITHYA .,M.SC.,M.PHIL.,(PH.D)
HEAD AND ASSOCIATE PROFESSOR
DEPARTMENT OF MATHEMATICS
SRI ADI CHUNCHANAGIRI WOMEN’S COLLEGE
CUMBUM.
Mail id : nithyarajkumar15@gmail.com

2. ABSTRACT
In this paper we shall take a brief look into the basic concepts, GSM mobile phone
network and graph coloring of network. The network graph theory has been extensively applied
in various application domains, such as Social network, Security etc…research on how to utilize
Graph theory in mobile networks remains limited up to now. This paper provides better network
and optimize its infrastructure investments. We also use GSM - Mobile Network, Definitions,
Examples, Communication network and its applications.

3. NETWORK GRAPH THEORY
INTRODUCTION:
Network graph theory is applicable to problems in communications, including multi-
hop wireless networks. Tremendous growth in the popularity of mobile communication services
has occurred worldwide. As a result, in our small spheres of everyday living, we are never far
from mobile communication services. Communication networks, including mobile are becoming
a new social infrastructure in many countries. Moreover, IT-based societies are expected to be
established to improve human life in many countries.

4. GSM-MOBILE PHONE NETWORK
INTRODUCTION:
GSM is a digital mobile network that is widely used by mobile phone users in
Europe and other parts of the world. GSM uses a variation of Time Division Multiple Access
(TDMA). It Operators at either the 900 MHZ or 1800 MHZ frequency band.
It was first implemented in Finland in December 1991. It became a standard for
mobile communications achieving over 90% market share, and operating in over 193 countries
and territories. The GSM Association estimated in 2011 that technologies defined in the GSM
standard served 80% of the mobile market, encompassing more than 5 billion people across more
than 212 countries and territories, making GSM the most ubiquitous of the many standards for
cellular networks.

5. DEFINITION
• The Global System for Mobile Communication is a standard developed by the European
Telecommunication Standard Institute (ETSI) to describe the protocols for second generation
(2G) digital cellular networks used by mobile devices such as mobile phones. Which stands for
GSM, regions as the world’s most widely used cell phone technology.
• A cellular network or mobile network communication is a telecommunications network where
the link to and from end nodes is wireless and the network is distributed over land areas called
cells, each served by at least one fixed-location transceiver. (e.g., mobile phones, tablets and
laptops).

6. CHARACTERISTICSOF GSM:
GSM makes use of narrowband Time Division Multiple Access (TDMA) technique for transmitting
signals. GSM was developed using digital technology. It has an ability to carry 6 kbps to 120 Mbps of data
rates. Presently GSM supports more than one billion mobile subscribers in more than 210 countries
throughout the world.
GSMARCHITECTURE:

7. 1. MOBILE STATION(MS):
• Mobile Equipment (ME)
• Subscriber Identity Module (SIM)
2. BASESTATIONSUBSYSTEM(BSS):
• Base Transceiver Station (BTS)
• Base Station Controller
3. NETWORKAND SWITHCINGSUBSYSTEM:
• Mobile Switching centre (MSC)
• Home Location Register (HLR)
• Visitor Location Register (VLR)
• Equipment Identity Register (EIR)
• Authentication Centre (AuC)
PUBLICSWITCHIEDTELEPHONENETWORK(PSTN)

8. 1. MOBILE STATION(MS):
MOBILEEQUIPMENT(ME)
• It is portable and hand held devices.
• It is uniquely identified by an IMEI (International Mobile Equipment Identity)
• It provides Voice and data transmission.
SUBSCRIBERIDENTITYMODULE(SIM):
• SIM is a smart card contains the International Mobile Subscriber Identity (IMSI)
• It allows users to send and receive calls and receive other subscribed services.

9. 2. BASESTATIONSUBSYSTEM(BSS):
Base Station Subsystem consists of two categories BTS, BSC.
BaseTransceiverStation(BTS)
• BTS sends and receives signals from mobile station
• It encodes, encrypts and modulates signals to the antenna
BaseStationController(BSC)
• Base Station Controller controls group of Base Transceiver Station.
• It handle call setup.

10. 3. NETWORKSUB-SYSTEM(NSS):
MobileSwitchingCentre(MSC)
• MSC is called as heart of the network.
• It communicates with HLR, VLR, EIR and AuC.
HomeLocationRegister(HLR)
• HLR stores information about each subscriber that belongs to its mobile switching.
• As soon as mobile subscriber leaves its current location, the information in the HLR is updated.
VISITERLOCATIONREGISTER(VLR)
• VLR is subset of Home Location Register.
• VLR is database which contains the exact location of all mobile subscribers currently present in
the service area of MSC. /

11. EQUIPMENTIDENTITYREGISTER(EIR):
• EIR database containing all valid mobiles on network using IMEI (International Mobile
Equipment Identity).
• It makes IMEI as invalid, if mobile is stolen.
AUTHENTICATIONNCENTRE(AuC)
• AuC protects network operators from fraud.
• It situated in special protected part of HLR.
PUBLICSWITCHIEDTELEPHONENETWORK(PSTN)
• Finally the signals from the Network Subsystem is send network to Public Switched Telephone
Network (PSTN).

12. COMMUNICATIONNETWORK
A communication network refers to how information flows within the organization. Information within an
Organization generally flows through a system. Communication networks are Regular patterns of person-to-
person relationships through which information flows in an organization.
TYPES OF COMMUNICATION NETWORK
• Vertical network
• Chain network
• Circuit network
• Wheel network
• Star network

13. VERTICALNETWORK:
Vertical network communication is sharing information hierarchically-from top to bottom or bottom to top.
This communication provides an immediate response as the receiver receives the information faster than any
Other network. We can call this network as a formal network.
CHAINNETWORK:
In a chain network individuals communicate in a set sequence. Here bottom to top communication does not
happen. Superiors ordering the subordinates is the best example of this type of network. The message has to
reach from top-level to bottom level.
CIRCUITNETWORK:
The communication is thus two people communicating with each other, sending messages and feedbacks
and thus forming a loop or a circuit. Here the communication is a two-way communication.
WHEELNETWORK:
This organization where there is a single controlling authority who gives instructions and orders to all
employees working under them. The information is received directly from the central authority, and the
communication is very powerful.
STARNETWORK:
A star network enable people to communicate with each other or with people who are involved in the same
process. A WhatsApp group which is related to work is a good example of Star network.

14. DEFINITIONS
 Graph coloring involves assigning colors to certain elements of a graph subject to certain restrictions
and constraints. In other words, the process of assigning colors to the vertices such that no two
adjacent vertexes have the same color is caller Graph coloring.
 An edge coloring of a graph is an assignment of “colors” to the edges of the graph so that no two
edges have the same color.
 Vertex coloring is an assignment of colors to the vertices of a graph G such that no two adjacent
vertices have the same color. No two vertices of an edge should be of the same color.
 The four color conjecture states that map on the surface of a sphere can be colored with only four
colors so that no two adjacent countries have the same color. Each country must consist of single
connected region adjacent countries are those having a boundary line (not merely a single point) in
common. The problem of deciding whether the four conjectures is true or false is called Four Color
Problem.
 A planer graph is a graph that can be embedded in the plane. It can be drawn on the plane in such a
way that its edges intersect only at their endpoints. It can be drawn in such a way that no edges cross
each other.

15. EXAMPLE:
A plane graph (geometric dual) can be associated with each map. Coloring the countries
of the map is equivalent to coloring the vertices of its Geometric dual. In this set up, the
four color conjecture states that “Every planar graph is 4-colourable”.
The number 4 cannot be reduced further as there are maps that require at least four
colors. There are several problems in graph theory that are equivalent to the color
problem.

16. Transportation (ROUTING)
Theone-waystreetproblem:
One of the problems faced by cities to control the flow of traffic is to ask whether it would be possible to
convert two-way streets into one-way streets without getting into trouble i.e., ending up with some places
that one can get into and never leave.
TheChinesepostmanproblem:
The Chinese postman problem, postman tour or route inspection problem is to find a shortest closed path
or circuit that Visits every edge of an (connected) undirected graph at least once. (Eulerian chain)
Travellingsalesmanproblem:
The salesman problem is used to describe a situation when a salesman wishes to visit in different cities,
each exactly once, and return to the starting point, in such a way as to minimize cost. (Hamiltonian graph)

17. APPLICATION OF MAP COLOURING USING GSM
• The Global System for Mobile (GSM) communication was created in 1982 to provide a standard for a
mobile telephone system. The first GSM network was launched in 1991 by RADIOLINJA in Finland.
Today, GSM is the most popular standard for mobile phones in the world, used by over 2 billion people
across more than 212 countries.
• GSM is cellular network with its entire geographical range divided into hexagonal cells. Each cell has a
communication tower which connects with mobile phones within the cell. All mobile phone Connect to
the GSM network by searching for cells in the immediate vicinity.
• GSM networks operate in only four different frequency ranges. The reason why only four different
frequencies suffice is clear. The map of the cellular regions can be properly colored by using only four
different colors. That is the map of India is colored with a minimum of four colors only. Here regions
sharing the same color to share the same frequency. so, the vertex coloring may be used for assigning at
most four different frequencies for any GSM mobile phone network.

18. Dual of Indian map
The cells of GSM

19. SERVICEONTHEGSMNETWORK:
• Telephone
• CSD (Circuit Switched Data, data transfer)
• SMS (Short Message Service)
• MMS (Multimedia Message Service)
• GPRS (General Packet Radio service)
BENEFITSOFGSM:
• As of 2010, there are over 3 billion people in 212 countries operating on the GSM standard understanding the
performance benefits of GSM helps to understand why over 80 percent of mobile phone across the world
operates on the GSM.
• This allows for easy exchange from one phone to another without new cell phone service activation GSM uses
digital technology and is a second generation (2G) cell phone system.

20. ADVANTAGES
• Low-cost mobile set and base stations.
• It improves spectrum efficiency.
• The data or voice signals are of high quality in GSM.
• The GSM is compatible with ISDN (Integrated Services Digital Network).

21. NODE COLOURING THEOREM
As can be seen in the map below, borders wander making it a difficult problem to analyze a map. Instead
of using a sophisticated map with many wandering boundaries, it becomes a simpler problem if we use
node coloring. If two nodes are connected by a line, then they can't be the same color. Wireless Service
providers employ node coloring to make an extremely complex network map much more manageable.

22. THANK YOU